devtools::install_github("cschwarz-stat-sfu-ca/Petersen",
dependencies = TRUE,
build_vignettes = TRUE)The Petersen-Estimator (and much more) for Two-Sample Capture-Recapture Studies with Applications to Fisheries Management
1 Installation & Change log
1.1 Installation
The Petersen package can be installed from CRAN in the usual way.
The development version can be installed from within R using:
1.2 Access to accompanying workbook
The accompanying workbook is available in the external data directory of the package and can copied to your working directory using:
extdata.dir <- system.file("extdata", package="Petersen")
extdata.dir[1] "/Users/cschwarz/Rlibs/Petersen/extdata"
extdata.list <- list.files(extdata.dir)
extdata.list[1] "PetersenWorkBook-2023-05-01.xls"
# Uncomment the following to copy the PetersenWorkbook to your working directory.
#file.copy(from=file.path(extdata.dir, "PetersenWorkbook-2006-01-20.xls"), to=getwd())1.3 Change log
Date | Changes |
|---|---|
2025-03-01 | Added n1_n2_m2_to_cap_hist() function to generate capture histories summary statistics |
2024-06-01 | Added new example of forward-reverse capture-recapture (lower Fraser coho) |
Added chapter on use of multimark when you have left and right photographs and cannot match left and right to the same animal. | |
2023-12-01 | Updates for CRAN submission. No new functionality or examples. |
2023-05-01 | First Release |
2 Introduction
In the late 1890’s, Petersen (1896) estimated exploitation probabilities and the abundance of fish living in enclosed bodies of water. His methods have been widely adopted and the Petersen-method is among the most widely used methods in fisheries management.
Similar methods were used by Laplace (1793) to estimate the population of France based on birth registries; by Lincoln (1930) to estimate the abundance of ducks from band returns; and by Jackson (1933) to estimate the density of tsetse flies.
The Petersen-method is the simplest of more general capture-recapture methods which are extensively reviewed in Williams et al. (2002). Despite the Petersen method’s simplicity, many of the properties of the estimator, and the effects of violations of assumptions are similar to these more complex capture-recapture studies. Consequently, a firm understanding of the basic principles learned from studying this method are extremely useful to develop an intuitive understanding of the larger class of studies.
The purpose of this monograph is to bring together a wide body of older and newer literature on the design and analysis of the “simple” two-sample capture-recapture study. This monograph builds upon the comprehensive summaries found in Ricker (1975), Seber (1982), Seber and Schofield (2023), and William et al (2002), and incorporates newer works that have not yet summarized. While the primary emphasis is on the application to fisheries management, the methods are directly applicable to many other situations.
Computer software has revolutionized many aspects of data analysis. A workbook accompanies this monograph to assist in the design and analysis of the Petersen studies. As well, the Petersen package in R is available for download.
Following Stigler’s law of eponymy https://en.wikipedia.org/wiki/Stigler%27s_law_of_eponymy, Goudie and Goudie (2007) investigated the origin of the Petersen estimator and identified additional scientists whose early work on marking and estimating fish populations deserves more credit than it has received.
3 Basic Sampling protocols and estimation
3.1 Conceptual basis
The fundamental goal of a Petersen study is to estimate \(N\), the number of animals (the abundance) in the population of interest.
The idealized protocol consists of an initial capture of \(n_1\) animals from the population. These animals are given a mark or tag (Figure 1).
Marks or tags fall into two general categories. Batch marks are simple marks that only identify that an animal was captured at a particular occasion. It is impossible to identify individual animals from batch marks. While batch marking is sufficient for the Petersen and other two-sample methods, modern practice is to use individually numbered tags so that the capture history of each individual animal can be determined and individual animals can be identified from each other.
The marked/tagged animals are then returned to the population. After allowing the marked and remaining unmarked animals to mix, a second sample of size \(n_2\) is selected. Each animal in the second sample is examined, and a count of the number of animals marked in the first sample and now recaptured, \(m_2\) is taken.
The summary statistics \(n_1\), \(n_2\), and \(m_2\) are sufficient statistics for this study. Modern practice is to record information in terms of capture histories rather than these summary statistics. A capture history, \(\omega\) is a vector where component \(i\) of the vector takes the value of \(1\) if an animal was captured at sampling event (time) \(i\) and the value \(0\) if the animal was not captured at the sampling event (time) \(i\). Because the Petersen study only has two capture occasions, all capture histories are of length 2 where:
- \(\omega=\{1,1\}\) represents an animal captured at both sampling occasions.
- \(\omega=\{1,0\}\) represents an animal captured at the first occasion but not at the second occasion.
- \(\omega=\{0,1\}\) represents an animal not captured at the first occasion but captured at the second occasion.
- \(\omega=\{0,0\}\) represents animals not captured at either sampling occasion (not observable).
The notation \(n_\omega\) represents the number of animals with capture history \(\omega\). Note that
- \(N=n_{\{0,0\}}+n_{\{0,1\}}+n_{\{1,0\}}+n_{\{1,1\}}\),
- \(n_1=n_{\{1,0\}}+n_{\{1,1\}}\),
- \(n_2=n_{\{0,1\}}+n_{\{1,1\}}\) and
- \(m_2=n_{\{1,1\}}\).
The capture history notation is especially convenient for more complex capture-recapture studies. Both notations will be used in this monograph.
The fundamental estimating equation is based on the idea that the proportion of marked animals in the second sample should be approximately equal to the proportion of animals initially captured:
\[\frac{m_2}{n_2} \approx \frac{n_1}{N}\]
By rearranging this relation, the Petersen estimator (Equation 1) is obtained
\[\widehat{N}_{Petersen} = \frac{n_1 n_2}{m_2} \tag{1}\]
The estimated capture probabilities at each sample occasion can also be obtained: \[\widehat{p}_1 = \frac{n_1}{\widehat{N}} = \frac{m_2}{n_2}\] \[\widehat{p}_2 = \frac{n_2}{\widehat{N}} = \frac{m_2}{n_1}\]
If \(\widehat{N}\) is to be a sensible estimator of \(N\), several assumptions must be made. The effects of violations of these assumptions will be discussed in Section 5.
Following Seber (1982) these assumptions are:
Closure. In other words, no animals leave the population (by death or emigration) and no animals enter the population (by internal births or immigration) between sampling occasions.
Homogeneity. This assumption can be satisfied in a number of ways. All animals have the same probability of capture at the first occasion, or all animals have the same probability of capture at the second occasion, or the second sample is a simple random sample selected from the entire population, i.e., each animals is captured or not captured independently of every other animal with the same probability. This assumption allows for some latitude in the study. For example, fish may be conveniently marked in the first sample without worrying about randomization if the scientist is sure that the second sample is a random sample from the entire population. Of course, it is likely wise to make such a strong assumption and randomization in each sample is highly recommended.
No impact of marking. Marking the animal does not affects its subsequent survival or catchability, i.e., all animals in the second sample, regardless of marking status, have the same probability of capture.
No tag loss. No marked animal loses its mark between the two sampling occasions.
No missed tags. All marked animals are correctly identified in the second sample.
3.2 Sampling protocols
While the estimator \(\widehat{N}\) in Equation 1 is intuitively appealing, its properties (bias and precision) cannot be investigated unless the sampling scheme that results in the observed data is fully specified. There are many sampling protocols, the most common being:
- Direct Sampling. In direct sampling method the sample sizes (\(n_1\) and \(n_2\)) are specified in advance.}
- Inverse sampling. In Inverse Sampling, sampling continues until a certain number of marks is obtained.
For each of these protocols, fish can be sampled with or without replacement giving:
- Hypergeometric Sampling. In this methods sampling occurs without replacement;
- Binomial sampling. In the binomial model (sampling with replacement); and
Modern statistical methods for capture-recapture data consider the number of animals in each capture history to be a realization of a multinomial distribution, which is a generalization of the binomial sampling methods.
3.3 Estimation
3.3.1 Maximum likelihood estimation
Once the sampling model has been established, the standard method of obtaining the estimator is Maximum Likelihood Estimation (MLE). The likelihood equations for the various sampling protocols is shown in Table 1.
Maximum Likelihood Estimators asymptotically unbiased and fully efficient (i.e., make use of all of the data and results in the smallest possible standard error). It turns out that for all the sampling schemes discussed above that the estimator \(\widehat{N}\) from Equation 1 is the MLE.
While the MLE is optimal in large samples, it can be severely biased with smaller sample sizes because of the presence of \(m_2\) in the denominator. Indeed, when \(E[m_2]\) is small, there is a fairly large probability that no marks would be observed (i.e., \(m_2=0\)) and \(\widehat{N}=\infty\). Chapman (1951) suggested a simple modification to the estimator as shown in Table 1. Add reference here to Rivest’s work on determining the optimal correction factor.
These modifications removes most of the bias, and Robson and Regier (1964) showed that the approximate residual bias (when \(n_1+n_2 < N\)) is \[b=E\left[\frac{\widehat{N}_{HU}-N}{N}\right] = E\left[- \exp \left( - \frac{(n_1+1)(n_2+1)}{N}\right)\right]\] If \(E[m_2]>4\), the residual relative bias is less than 2% of the abundance. To allow for variation in the observed \(m_2\) around its expected value, Robson and Regier (1964) recommend that studies have \(m_2>7\) to be 95% confident that the \(E[m_2]>4\) and that the residual relative bias in \(\widehat{N}_{HU}\) is negligible. This is equivalent to ensuring that \(n_1 n_2 > 4N\) as outlined by Robson and Regier (1964).
| Sampling Model | Likelihood | Bias adjusted estimator | Estimated variance |
|---|---|---|---|
| Direct Hypergeometric | \(\frac{\binom{n_1}{m_2} \binom{N-n_1}{n_2-m_2}}{\binom{N}{n_2}}\) | \(\widehat{N} _{HU}=\frac{(n_1+1)(n_2+1)}{(m_2+1)}-1\) | \(\widehat{v}_{HU} = \frac{(n_1+1)(n_2+1)(n_1-m_2)(n_2-m_2)}{(m_2+1)^2(m_2+2)}\) |
| Direct Binomial | \(\binom{n_2}{m_2}\left(\frac{n_1}{N}\right)^{m_2}\left( 1-\frac{n_1}{N}\right)^{n_2-m_2}\) | \(\widehat{N}_{BU} = \frac{n_1(n_2+1)}{m_2+1}\) | \(\widehat{v}_{BU} = \frac{n_1^2 (n_2+1) (n_2-m_2)}{(m_2+1)^2 (m_2+2)}\) |
| Inverse Hypergeometric | \(\frac{\binom{n_1}{m_2-1}\binom{N-n_1}{n_2-m_2}}{\binom{N}{n_2-1}} \times \frac{n_1-m_2+1}{N-n_2+1}\) | \(\widehat{N}_{IHU} = \frac{(n_1+1)n_2}{m_2}-1\) | to be added later |
| Inverse Binomial | \(\binom{n_2-1}{m_2-1} \left(\frac{n_1}{N}\right)^{m_2}\left( 1-\frac{n_1}{N}\right)^{n_2-m_2}\) | \(\widehat{N}_{IBU} = \frac{n_1 n_2}{m_2}\) | \(\widehat{v}_{IBU} = \frac{n_1^2 n_2 (n_2-m_2)}{m_2^2(m_2+1)}\) |
| Capture History Multinomial | \(\binom{N}{n_{00},n_{01},n_{10},n_{11}} \times\) \(\left( (1-p_1)(1-p_2) \right)^{n_{00}} \times\) \(\left( p_1(1-p_2) \right)^{n_{10}} \times\) \(\left( (1-p_1)p_2 \right)^{n_{01}} \times\) \(\left( p_1 p_2 \right)^{n_{11}}\) | \(\widehat{N}_{MN} = \frac{{\left( {n_{11} + n_{10} } \right)\left( {n_{11} + n_{01} } \right)}}{{n_{11} }} =\) \(\frac{{n_1 n_2 }}{{m_2 }}\) | \(\widehat{v}_{MN} = \frac{{n_1 n_2 }}{{m_2 }}\frac{{\left( {n_2 - m_2 } \right)}}{{m_2 }}\frac{{\left( {n_1 - m_2 } \right)}}{{m_2 }}\) |
Chapman (1951) also derived the variance of the hypergeometric estimator and expressed it as: \[V \left( \widehat{N}_{HU} \right) = N^2 \left( E[m_2]^{-1} + 2E[m_2]^{-2} + 6E[m_2]^{-3} \right)\] If \(E[m_2]\) is small, then the variance is large. For example if \(E[m_2]=10\), then the relative standard error (\(RSE=\frac{SE}{estimate})\)) is over 35% and a 95% confidence interval will only be accurate to within 70% of the true value of \(N\)! A discussion of sample size requirements is presented in Section 4.
In cases where the marked fraction is very small (i.e., \(n_1 << N\)) or when sampling is done with replacement (e.g. when animals are observed rather than physically captured), the binomial model of Bailey (1951, 1952) may be used as summarized in Table 1. Seber (1982, p. 61) also points out that the Bailey estimator may be appropriate when complete mixing of marked and unmarked animals takes places and a systematic sample rather than a simple random sample is taken. The Bailey adjusted estimator has comparable residual bias to the Chapman adjusted estimator and is not reported here. In most practical situations, there is little difference between the hypergeometric and binomial sampling model estimates or estimated variances.
In inverse sampling, the number of recaptures (\(m_2\)) to be obtained is fixed in advance and the size of the second sample (\(n_2\)) is now random. This was considered by Bailey (1951), Chapman (1951), Robson (1979); summarized by Seber (1982, Section 3.8); and results are presented in Table 1. Both inverse sampling methods are more efficient (i.e., for a given precision of the estimated abundance, the expected sample size required to obtain this precision under inverse sampling is smaller than that required under direct sampling) than their direct sampling counterparts, but the gain in efficiency is, in practice, negligible. The primary disadvantage of inverse sampling is that with poor planning, the expected sample size could be very large. Seber (1982) summarizes an alternate sampling scheme in which the number of unmarked individuals captured in the second sample is fixed.
Seber (1982) discusses the case of random sample sizes and notes that in practice one would condition upon the observed values so that these previous models are still appropriate. One can also think of a model where the number of fish in the four possible tag histories is random which naturally evolves into more complex studies with multi-samples from both open and closed populations.
In the multinomial model, the counts in the four possible capture histories is considered to arrive from a multinomial model. This multinomial model is the predominant paradigm in current capture-recapture methodology and will be used in the remainder of this monograph. The derivation of the results under the multinomial sampling protocol is found in Section 18.1 and the results are also summarized in Table 1.
In some cases, despite best efforts, no recapture are observed, i.e., \(m_2=0\). While the MLE is nonsensical, the adjusted estimators of Table 1 do provide “estimates” but these will be of very poor precision. Alternatively, Bell (1974) showed that under the hypergeometric sampling model \[P(m_2=0) = \frac{(N-n_1)! (N-m_2)!}{N! (N-n_1-n_2)!}\] and suggested solving \(P(m_2=0)=.5\) as an estimator of \(N\) with the solutions to \(P(m_2=0)=.025\) and \(P(m_2=0)=.975\) as 95% confidence bounds for \(N\). While this works in theory, the resulting estimator has such poor precision that the practical application of this results is doubtful.
Finally, it should be noted, that most sampling plan do not fall exactly into any of the above categories. In many practical plans, the amount of effort (e.g. person-days) is specified for both the initial and second sample, and the number of fish that are captured depends on chance events within that period of effort and should be considered random.
In most studies, results from any of the estimators are similar enough that the practitioner should not be too concerned about the choice of appropriate model – error in the estimates attributable to other problems in the experiment such as assumptions not being satisfied exactly will likely be an order of magnitude greater than any differences in estimates of abundance or precision among the model formulations.
3.3.2 Conditional likelihood estimation
While the MLE are fully efficient, an alternate estimator can be derived that conditions on the observed fish only. Huggins (1989) provides the theory for the conditional multinomial which uses only the observed fish to estimate catchabilities and abundance is estimated using a Horvitz-Thompson type estimator (Section 18.2)
Its main usage is when catchability depends upon individual covariates (e.g., fish length) which is unknown for fish never caught.
In the case of no individual covariates, the conditional likelihood estimators reduce to the full likelihood estimators with no loss of efficiency (i.e., same standard errors), so in practice, the conditional likelihood approach can always be used and is the basis for estimators found in the Petersen package. See Section 18.2 for more details.
3.3.3 Confidence intervals
Confidence intervals for the abundance can be computed in a number of ways.
3.3.3.1 Large sample Wald interval
This method relies upon the asymptotic normality of \(\widehat{N}\) and the usual large-sample, asymptotic, normal-theory based confidence interval is: \[\widehat{N} \pm z_{\alpha/2} SE_{\widehat{N}}\]
However, this interval is not recommended for standard usage for two reasons:
- The distribution of \(\widehat{N}\) is typically skewed with a long right tail;
- There is a very strong positive correlation between \(\widehat{N}\) and the estimated \(SE\). This implies that when \(\widehat{N}\) is below the true population value, the \(SE\) tends to also be smaller than the true \(SE\) and the resulting confidence interval is too narrow, and vice verso.
Many authors have suggested modifications to improve upon the large-sample asymptotic result above.
3.3.3.2 Logarithmic transform
Programs such as MARK compute a confidence interval on the logarithm of \(\widehat{N}\) and then invert the corresponding interval.
\[ \widehat{\theta} = \log{\widehat{N}}\] \[ se_{\widehat{\theta}} = \frac{se_{\widehat{N}}}{\widehat{N}}\] The confidence interval for \(\log{\widehat{N}}\) is found as \[\widehat{\theta} \pm z_{\alpha/2} se_{\widehat{\theta}}\] and then the confidence interval for \(\widehat{N}\) is found by re-inverting the above interval \[\exp{(\widehat{\theta} - z_{\alpha/2} se_{\widehat{\theta}})}~ to~ \exp{(\widehat{\theta} + z_{\alpha/2} se_{\widehat{\theta}})}\]
3.3.3.3 Inverse transformation
Ricker (1975) suggest first using a simple inverse transform, then finding a confidence interval based upon \(1/\widehat{N}\), and then re-inverting the resulting confidence interval, i.e., first compute:
\[ \widehat{\theta} = \frac{1}{\widehat{N}}\] \[ se_{\widehat{\theta}} = \frac{se_{\widehat{N}}}{\widehat{N}^2}\] Then find a confidence interval for \(1/N\) based upon the transformed values, \[\widehat{\theta} \pm z_{\alpha/2} se_{\widehat{\theta}}\] and finally then the confidence interval for \(\widehat{N}\) is found by re-inverting the above interval \[\frac{1}{\widehat{\theta} + z_{\alpha/2} se_{\widehat{\theta}}}~ to ~ \frac{1}{\widehat{\theta} - z_{\alpha/2} se_{\widehat{\theta}}}\]
3.3.3.4 Inverse cube-root transform
The inverse approximation above appears to work fairly well, but Sprott (1981) used likelihood theory to show that the inverse-cube-root transform more effectively captured the skewness in the sampling distribution. His procedure is very similar to the above: \[ \widehat{\theta} = \frac{1}{\widehat{N}^{\frac{1}{3}}}= \frac{1}{\sqrt[3]{\widehat{N}}}\] \[ se_{\widehat{\theta}} = \frac{se_{\widehat{N}}}{3 \widehat{N}^{4/3}}\] The confidence interval for \(1/N^{1/3}\) is found as \[\widehat{\theta} \pm z_{\alpha/2} se_{\widehat{\theta}}\] and then then the confidence interval for \(\widehat{N}\) is found by re-inverting the above interval \[\frac{1}{(\widehat{\theta} + z_{\alpha/2} se_{\widehat{\theta}})^3}~ to \frac{1}{(\widehat{\theta} - z_{\alpha/2} se_{\widehat{\theta}})^3}\]
3.3.3.5 Bootstrapping
Bootstrapping is easy to implement when data is collected as capture-histories (rather than the summary statistics) because each fish is represented by an individual capture history. A resampling of the capture-histories then represents a bootstrap sample; estimates can be computed for each bootstrap sample, and the usually methods for determining confidence intervals from bootstrap samples can be used.
3.3.3.6 Bayesian credible intervals
Add more details later
3.3.3.7 Profile intervals
While the transformation methods have the advantage of simplicity with the computations easily done by hand, a likelihood method uses the likelihood function directly to capture the skewness. Standard likelihood theory shows that the profile confidence interval is found by finding all values of \(N\) such that: \[-2 l(N) - 2 l(\widehat{N}) \le \chi^2_{\alpha}\]
However, in the conditional likelihood methods. \(N\) does NOT appear directly in the likelihood and so these methods are not relevant
3.3.3.8 Which method to choose?
All transformation methods should give similar results when the number of marks returned is reasonable. The methods could give quite different answers in cases when only a few marks are returned (say less than 20). However, in these cases, the differences in results among the confidence interval methods is small relative to the (unknown) biases and uncertainties from assumptions failures (such as non-mixing) that are still resident in the study.
The Petersen package created for this monograph used the logarithmic transformation to compute the confidence intervals for \(N\).
It should be noted that confidence intervals only capture the uncertainty in the estimate due to sampling – it does NOT capture uncertainty due to failure of assumptions, problems in the study, or other problems with the study.
3.4 Software
A simple internet search will find much software that can compute the Petersen estimator because the computations are so simple. However, these packages seldom take a coherent modeling strategy for the more complex models for Petersen studies. Similarly, the data structures seldom are consistent with modern software for capture-recapture studies (e.g., MARK).
Consequently, the Petersen R package has been developed to use a consistent methodology (conditional maximum likelihood estimation) with a consistent data frame work (capture histories). This package is available from the usual R repositories.
The VGAM (Yee et al., 2015) package also adopts the conditional likelihood approach for the closed population models with 2+ sample times, of which Petersen studies are simple cases. The use of this package is illustrated in Section 19.
The MARK program (and RMark which calls MARK) could be used for the simple Petersen studies, including the conditional likelihood approach. The use of this package is illustrated in Section 20.
3.5 Example - Estimating the number of fish in Rödli Tarn
Ricker (1975) gives an example of work by Knut Dahl on estimating the number of brown trout (Salmo truitta) in some small Norwegian tarns. Between 100 and 200 trout were caught by seining, marked by removing a fin (an example of a batch mark) and distributed in a systematic fashion around the tarn to encourage mixing. A total of \(n_1=109\) fish were captured, clipped and released, \(n_2=177\) fish were captured at the second occasion, and \(m_2=57\) marked fish were recovered.
The data are available in the data_rodli data frame in the Petersen package and can be accessed in the usual fashion:
library(Petersen)
data(data_rodli)
data_rodli
## cap_hist freq
## 1 11 57
## 2 10 52
## 3 01 120The data frame consists of (at least) two columns:
- a variable cap_hist with the two digit capture history (a character vector) -
- a variable freq that contains the number of fish in each capture history.
Additional columns can be present in the data frame for attributes of the fish such as sex, length etc.
The data frame can have a separate row for each fish (each with freq=1), or a summary as shown above.
You can construct the capture histories from the summary statistics as shown below:
cap_hist <- Petersen::n1_n2_m2_to_cap_hist( n1=109, n2=177, m2=57)
cap_hist cap_hist freq
1 10 52
2 01 120
3 11 57
3.5.1 Petersen estimate
We find the Petersen estimator of abundance using the conditional likelihood approach used in the Petersen package in two steps (the reason for the two steps will be explained later):
In the first step, the conditional-likelihood model is fit to the data:
rodli.fit.mt <- Petersen::LP_fit(data_rodli, p_model=~..time)The LP_fit() function takes the data frame of capture histories seen earlier and a model for the capture probabilities (the p_model argument). The model for the capture probabilities can refer to any variable in the data frame (e.g., sex) or to several special variables such as ..time which refer to the two time periods. Some knowledge of how R sets up the design matrix given the data frame is helpful in deciding how to specify p_model in more complex situations involving stratification and is discussed later.
In the standard Petersen estimator, we allow the capture probabilities to vary across the two sampling events. Consequently, the p_model was specified as p_model=~..time.
A summary of the fit is given in a data frame
rodli.fit.mt$summary
## p_model name_model cond.ll n.parms nobs method
## 1 ~..time p: ~..time -233.9047 2 229 cond llThe value of the conditional likelihood, number of parameters in the conditional likelihood (just the two capture probabilities) and the number of observed fish (sum of the freq column) are also presented. Notice that in the conditional likelihood approach, the abundance is NOT a parameter in the likelihood and so is not counted in the model summary table.
In the second step, we obtain estimates of overall abundance using the LP_est() function and the N_hat argument. Here there is no stratification or other groupings of the data, so the formula for N_hat is ~1 indicating that we should find the estimated abundance for the entire population. (In later sections, we will obtain abundance estimates for individual strata as well).
rodli.est.mt <- Petersen::LP_est(rodli.fit.mt, N_hat=~1)This again gives a data frame with the estimated abundance.
rodli.est.mt$summary
## N_hat_f N_hat_rn N_hat N_hat_SE N_hat_conf_level N_hat_conf_method
## 1 ~1 (Intercept) 338.4737 25.49646 0.95 logN
## N_hat_LCL N_hat_UCL p_model name_model cond.ll n.parms nobs method
## 1 292.0154 392.3232 ~..time p: ~..time -233.9047 2 229 CondLikThe estimated abundance is 338 (SE 25) fish computed as:
\(\widehat{N}=\frac{109 \times 177}{57}=338\).
The 95% confidence interval for \(N\) was computed using a logarithmic transformation is 292 to 392 fish.
The relative standard error (RSE) is found as \[RSE =\frac{SE}{estimate}=\frac{25.5}{338.5}=.075\]
is similar to the approximation that \[RSE \approx \frac{1}{\sqrt(marks~recovered)}=\frac{1}{\sqrt{57}}=.13\]
While the process of specifying a model for the capture probabilities and for the abundance estimate may seem a bit convoluted, its real power will become apparent when more complex cases involving stratification are discussed later.
3.5.2 Applying a bias correction
The Chapman modifications can be applied as outlined in Table 1. This can be implemented by adding a single “new” fish with capture history “11” to the existing data frame.
data(data_rodli)
rodli.chapman <- plyr::rbind.fill(data_rodli,
data.frame(cap_hist="11",
freq=1,
comment="Added for Chapman"))
rodli.chapman
## cap_hist freq comment
## 1 11 57 <NA>
## 2 10 52 <NA>
## 3 01 120 <NA>
## 4 11 1 Added for ChapmanThen this adjusted data is passed to the Petersen package and the two step procedure is again followed:
rodli.fit.mt.chap <- Petersen::LP_fit(rodli.chapman, p_model=~..time)
rodli.est.mt.chap <- Petersen::LP_est(rodli.fit.mt.chap, N=~1)rodli.est.mt.chap$summary
## N_hat_f N_hat_rn N_hat N_hat_SE N_hat_conf_level N_hat_conf_method
## 1 ~1 (Intercept) 337.5861 25.02396 0.95 logN
## N_hat_LCL N_hat_UCL p_model name_model cond.ll n.parms nobs method
## 1 291.9364 390.374 ~..time p: ~..time -235.2889 2 230 CondLikThe bias-corrected estimate of the abundance is 338 (SE 25) fish.
3.5.3 A model with equal capture probabilities
It is also possible to fit a model where the capture probabilities are equal at both sampling events. This is specified by changing the specification for the model for \(p\) from \(p=\sim ..time\) to \(p=\sim 1\):
rodli.fit.m0 <- Petersen::LP_fit(data_rodli, p_model=~1)
rodli.est.m0 <- Petersen::LP_est(rodli.fit.m0, N_hat=~1)This gives the estimates:
rodli.est.m0$summary
## N_hat_f N_hat_rn N_hat N_hat_SE N_hat_conf_level N_hat_conf_method
## 1 ~1 (Intercept) 358.7542 28.57733 0.95 logN
## N_hat_LCL N_hat_UCL p_model name_model cond.ll n.parms nobs method
## 1 306.8971 419.3738 ~1 p: ~1 -247.7207 1 229 CondLikNow the estimated abundance is 359 (SE 29) fish.
However, a comparison of the model fits using AICc (Table 2), shows that this model has much less support than the traditional estimator with unequal capture probabilities:
rodli.aictab <- Petersen::LP_AICc(
rodli.fit.mt,
rodli.fit.m0)Model specification | Conditional log-likelihood | # parms | # obs | AICc | Delta | AICcWt |
|---|---|---|---|---|---|---|
p: ~..time | -233.9047 | 2 | 229 | 471.86 | 0.00 | 1.00 |
p: ~1 | -247.7207 | 1 | 229 | 497.46 | 25.60 | 0.00 |
Notice the \(N\) is not part of the conditional likelihood and so is not counted as a parameter.
In general, models with equal capture probability over sampling events are seldom sensible from a biological perspective.
4 Planning studies
Before determining the amount and distribution of effort to be allocated in a capture-recapture study, one must first decide what level of precision is required from the study. In many cases, a desired measure of the relative precision (relative standard error) is a goal of the study.
Some papers use the term coefficient of variation (\(cv\)) to refer to the relative standard error. The term relative standard error is preferred and the term \(cv\) is reserved for describing the variability of individual data values, i.e., \(cv = \frac{std~dev}{mean}\).
In turn, the relative standard error can be used to express the relative 95% confidence interval using the approximate rule that the relative confidence interval is about \(\pm 2\) relative standard errors.
Seber (1982, p. 64) gives three target levels of precision that are commonly used:
- For preliminary surveys where only a rough idea of the abundance is needed, the relative 95% confidence interval should be \(\pm 50\%\) of the estimated abundance with a corresponding relative standard error of 25%. For example, it would be sufficient for a preliminary survey to have results with an estimate of 50 ( \(SE\) 12) thousand fish with a 95% confidence interval of between 25 and 75 thousand fish.
- For accurate management work, the relative 95% confidence interval should be \(\pm 25\%\) of the estimated abundance with a corresponding relative standard error of 12.5%. For example, it would be sufficient for accurate management work to have results with an estimate of 50 ( \(SE\) 6) thousand fish, with a 95% confidence interval between 38 and 62 thousand fish.
- For careful scientific research, the recommended relative confidence interval is \(\pm 10\%\) of the estimated abundance with a corresponding relative standard error of 5%. For example, it would be sufficient for scientific work to have results with an estimate of 50 ( \(SE\) 2.5) thousand fish, with a 95% confidence interval of between 45 and 55 thousand fish.
If \(\widehat{N}\) is to be used for further computations, e.g. splitting the population by size categories or multiplied by average biomass to obtain an estimate of total biomass, then a high degree of precision is required so that the precision of the final answer is adequate.
As a rough rule of thumb, the relative precision (relative standard error) of the Petersen estimate is proportional to \(\frac{1}{\sqrt{m_2}}\), i.e., to the square root of the number of marks returned. This can be used for planning purposes. For example, if the initial abundance is about 50,000 fish, and if 5,000 fish are marked and 1,000 fish are examined for marks, then the approximate number of marks recaptured is: \[E[m_2] \approx 5,000 \times \frac{1,000}{50,000} = 100\] and the approximate relative standard error will be on the order of \[rse \approx \frac{1}{\sqrt{100}} = .1\] This will give a relative 95% confidence interval of about \(\pm 20\%\) which should be precise enough for management purposes. In general, the three levels of precision will require a certain number of marks returned as summarized in Table 3:
| Preliminary | Management | Scientific | |
|---|---|---|---|
| 95% relative ci | \(\pm\) 50% | \(\pm\) 25% | \(\pm\) 10% |
| Relative SE | 25% | 12% | 5% |
| Required \(E[m_2]\) | 16 | 64 | 400 |
The rule of thumb can be inverted to estimate the approximate fraction of the population that needs to be marked assuming equal sample sizes at both sampling occasions. In this case, \(E[m_2] \approx n^2/N \approx Nf^2\), where \(f\) is the sampling fraction. Consequently, if scientific precision is needed (a relative standard error of 5% with 400 marks needed to be recaptured), then a population of 10,000 will require \(10,000 f^2 = 400\) or \(f=.2=20\%\) of the population will needed to be sampled on both occasions.
While these rules of thumb should be sufficient for most purposes, one could actually use the estimated variances presented earlier. The workbook that accompanies this monograph has a worksheet where the scientist can enter various values of \(N\), \(n_1\), and \(n_2\) to see the approximate expected precision that will be obtained. For example, Figure 2, shows that for a abundance of about \(N=50,000\), sample sizes of \(n_1=3,000\) and \(n_2=1,000\) would give a relative standard error of about 12% and a relative 95% confidence interval of about \(\pm 25\%\) which should be sufficient for management purposes.
Robson and Regier (1964) gave nonograms which have been adopted and are presented in this monograph in Figure 3 to Figure 5. For example, using Figure 4 for a abundance of \(N=50,000\), the following pairs of sample sizes will be required to have the 95% relative confidence interval to be within \(\pm 25\%\): \[(1,000; 3,000), (800; 4,000), (300; 10,000)\] The charts are symmetric in \(n_1\) and \(n_2\), so that the same precision is obtained for \(N=50,0000\) with \((n_1=1,000; n_2=3,000)\) fish and \((n_1=3,000; n_2=1,000)\) fish.
While Robson and Regier (1964) and Seber (1982) have nomograms for abundances less than 200, these are rarely useful in practice.
The above spreadsheets and nonograms are sufficient for most planning purposes, but it should be kept in mind that these computations assume that the study will proceed perfectly and that all assumptions will be satisfied. This is rarely the case in most surveys, and so the required effort should be increased to account for potential problems down the road.
The above charts also assume that the cost of sampling per fish is equal at both sampling occasions. If the costs of sampling per fish differ at each sampling occasion, then Robson and Regier (1964) and Seber (1982, p. 69) show that the optimal allocation of effort between the two sampling occasions is the solution to:
\[\frac{c_1 n_1}{c_2 n_2} = \frac{N- n_2}{N- n_1} \tag{2}\]
where \(c_1\) and \(c_2\) are the costs of sampling per fish at the two occasions. In many cases, the sample sizes are negligible compared to the abundance so the right hand side of Equation 2 is 1, and the optimal allocation reduces to spending equal amounts of money at the two sampling occasions.
5 Assumptions and effects of violations
5.1 Introduction
The Petersen estimator makes a variety of assumptions and virtually no real study satisfies all of the assumptions. Consequently, a study of the effect of violations of assumptions upon the performance of the estimator is helpful in deciding how much credence should be placed upon the results.
In the sections that follow, the effect of violations of assumptions will be studied by substituting in the expected value of the statistics under the assumption violation. While this yields only an approximate answer to the effect of the violation, the results are sufficiently accurate to be useful in understanding.
In the workbook that accompanies this monograph, a specialized spreadsheet has been set up where the various effects (both individually and combined) can be studied without worrying about the hand computations (Section 5.7).
This is useful in order to see if violations of assumptions will lead to unacceptable bias. As suggested by Cochran (1977, p. 12-15), bias can typically be ignored if it is less than 10% of the standard error of the estimator.
There have been many papers that demonstrate how to modify the Petersen study to check for assumption violations and adjust the estimator – some of these are studied in future sections.
An ad-hoc adjustment can be made to the basic Petersen estimator if information is available about an assumption violation, e.g., an estimate of tag retention with accompanying SE. This is implemented in the LP_est_adjust() function as illustrated in Section 5.8.
5.2 Non-closure
The Petersen estimator assumes that the population of interest is closed. This means that no animals leave the population between the two sampling occasions through death or emigration, and no animals enter the population between the two sampling occasions through immigration or birth.
5.2.1 Immediate handling mortality
For many species, the act of catching and marking the fish traumatic and some fish suffer immediate mortality. In this case, the number of deaths is known. The study population should be reduced by these known mortalities and the resulting estimator should be conditional upon the actual number of fish released with tags rather than those captured.
The effect of marking upon subsequent mortality will be considered in Section 5.3.
5.2.2 Natural mortality or emigration
Suppose that natural mortality or emigration takes place between the two sampling occasions. These two types of non-closure are indistinguishable and shall be referred to as mortality in the remainder of this section.
What is the effect of this natural mortality if both the marked and unmarked fish have the same average survival probability between the two sampling occasions?
Let \(\phi\) represent the average survival probability between the two sampling occasions. Then
- \(E\left[{n_1} \right] \approx N p_1\)
- \(E\left[{n_2} \right] \approx \left[ {N p_1 \phi + N(1-p_1)\phi} \right] p_2\)
- \(E\left[{m_2} \right] \approx n_1 \phi p_2 = N p_1 \phi p_2\)
and
\[E[\widehat N] \approx \frac{{E\left[ {n_1 } \right]E\left[ {n_2 } \right]}}{{E\left[ {m_2 } \right]}} = \frac{{Np_1 \times N\phi p_2 }}{{Np_1 \phi p_2 }} = N\]
i.e., the estimator remains essentially unbiased for the abundance at the time of the first sampling occasion.
In many cases, the mortality probability varies among groups (strata) of the population, e.g., different mortalities across different age groups. If the marked fish can be divided into groups (strata), a simple \(2 \times K\) contingency table can be constructed as shown in Table 4.
| \(A\) | \(B\) | \(\ldots\) | \(K\) | Total | |
|---|---|---|---|---|---|
| Number released | \(n_{1A}\) | \(n_{1B}\) | \(\ldots\) | \(n_{1K}\) | \(n_1\) |
| Recaptured | \(m_{2A}\) | \(m_{2B}\) | \(\ldots\) | \(m_{2K}\) | \(m_2\) |
| Not recaptured | \(n_{1A}-m_{2A}\) | \(n_{1B}-m_{2B}\) | \(\ldots\) | \(n_{1K}-m_{1K}\) | \(n_1-m_2\) |
The usual \(\chi^2\) statistic is computed and is used to test if the product of survival and subsequent recapture (\(\phi_x p_{2x}\)) are equal across all groups (strata). If the hypothesis is rejected , then this MAY be evidence that the mortality probabilities are different in the subgroups – however it could also be evidence that the recapture probabilities are also unequal in the second sample across groups.
5.2.3 Immigration or births
Closure can also be violated by the addition of new animals, either by immigration from outside the study area or natural “births” (e.g., fish recruiting through growth). As both cases are indistinguishable, the term immigration will be used to refer to any increase in the population between the two sampling occasions.
Let \(\lambda\) be the rate of population increase between the two sampling occasions, i.e., an average of \(\lambda\) new fish enter the population per member of the original population. Then
- \(E\left[{n_1} \right] \approx N p_1\)
- \(E\left[{n_2} \right] \approx N \lambda p_2\)
- \(E\left[{m_2} \right] \approx n_1 \phi p_2 = N p_1 \phi p_2\)
and \[ \begin{array}{c} E[\widehat{N}] \approx \frac{{E\left[ {n_1 } \right]E\left[ {n_2 } \right]}}{{E\left[ {m_2 } \right]}} = \frac{{Np_1 \times N\lambda p_2 }}{{Np_1 p_2 }} \\ = N\lambda = N_2 \\ \end{array} \] i.e., the Petersen estimator is approximately unbiased for the abundance at the second sampling occasion.
In many cases, recruitment varies across different groups of the population, e.g., smaller ages may tend to recruit as they get older between the two sample occasions.
If the fish recovered in the second sample can be divided into groups (strata), a simple \(2 \times K\) contingency table can be constructed as shown in Table 5.
| \(A\) | \(B\) | \(\ldots\) | \(K\) | Total | |
|---|---|---|---|---|---|
| Number captured | \(n_{2A}\) | \(n_{2B}\) | \(\ldots\) | \(n_{2K}\) | \(n_2\) |
| Marked | \(m_{2A}\) | \(m_{2B}\) | \(\ldots\) | \(m_{2K}\) | \(m_2\) |
| Not marked | \(n_{2A}-m_{2A}\) | \(n_{2B}-m_{2B}\) | \(\ldots\) | \(n_{2K}-m_{1K}\) | \(n_2-m_2\) |
The usual \(\chi^2\) statistic is computed and is used to test if the marked fraction are equals across all groups (strata). If the hypothesis is rejected , then this MAY be evidence of differential recruitment into the groups.
Seber (1982) has a non-parametric test for recruitment using length
5.2.4 Both immigration and mortality
Of course, both immigration and mortality can be occurring simultaneously.
As before, let \(\phi\) represent the average survival probability between the two sampling occasions, and let \(\lambda\) represent the net recruitment per individual alive at the start of the study before any mortality occurs. Then
- \(E\left[{n_1} \right] \approx N p_1\)
- \(E\left[ {n_2 } \right] \approx \left[ {N\left( {\lambda - 1} \right) + N\phi } \right]p_2\)
- \(E\left[{m_2} \right] \approx n_1 \phi p_2 = N p_1 \phi p_2\)
and \[ \begin{array}{c} E[\widehat{N}] \approx \frac{{E\left[ {n_1 } \right]E\left[ {n_2 } \right]}}{{E\left[ {m_2 } \right]}} = \frac{{Np_1 \times \left[ {N\left( {\lambda - 1} \right) + N\phi } \right]p_2 }}{{Np_1 \phi p_2 }} = \frac{{N[\lambda - 1 + \phi ]}}{\phi } \\ \end{array} \]
i.e., the estimator now estimates the total number of animals ever alive over the course of the study being a combination of the initial abundance and the net number of recruits..
5.3 Marking has no effect
The physical act of marking a fish can be very traumatic to individual fish. Marking effects usually take two forms (both of which may be present in a study) (a) a change in subsequent survival or (b) a change in subsequent catchability.
5.3.1 Marking affects survival
Both an acute effect (immediate mortality after release) and a chronic effect (no immediate mortality but increased mortality between the two sampling occasions compared to unmarked fish) can be handled in the same way.
Let \(\phi\) represent the survival probability for unmarked fish between the two sampling occasions, and \(\phi '\) represent the survival probability for marked fish between the two sampling occasions.
Then
- \(E\left[{n_1} \right] \approx N p_1\)
- \(E\left[ {n_2 } \right] = \left[ {Np_1 \phi ' + N\left( {1 - p_1 } \right)\phi } \right]p_2\)
- \(E\left[ {m_2 } \right] = Np_1 \phi 'p_2\)
and \[ \begin{array}{c} E[\widehat{N}] \approx \frac{{E\left[ {n_1 } \right]E\left[ {n_2 } \right]}}{{E\left[ {m_2 } \right]}} = \frac{{Np_1 \times \left[ {Np_1 \phi ' + N\left( {1 - p_1 } \right)\phi } \right]p_2 }}{{Np_1 \phi 'p_2 }} = N\left[ {\frac{\phi }{{\phi '}} + p_1 \left( {1 - \frac{\phi }{{\phi '}}} \right)} \right] \\ \end{array} \]
If the two survival probabilities are equal, then the ratios of survival probabilities are all equal to 1 and the estimator gives the number alive at the first sampling occasion as seen earlier. If the survival probability of marked fish is lower than the survival probability of unmarked fish, then the ratios are all greater than 1, and the Petersen estimator over estimates the number of fish. This is intuitive as increased mortality among the the marked fish leads to fewer marked fish being recaptured than expected and an inflation in the estimate.
In many studies \(p_1\) is small, and so the approximate relative bias is a function of the ratio of the two survival probabilities.
5.3.2 Marking affect catchability
The marking effect could affect subsequent catchability of the fish. This is often seen in small mammal studies where animals become trap happy or trap shy.
Let \(p_2\) represent the catchability at the second sampling occasion for unmarked fish, and \(p_2^{*}\) represent the catchability at the second sampling occasion for marked fish. Then
- \(E\left[{n_1} \right] \approx N p_1\)
- \(E\left[ {n_2 } \right] = Np_1 p_2 ' + N\left( {1 - p_1 } \right)p_2\)
- \(E\left[ {m_2 } \right] = Np_1 p_2 '\)
and
\[ \begin{array}{c} E[\widehat{N}] \approx \frac{{E\left[ {n_1 } \right]E\left[ {n_2 } \right]}}{{E\left[ {m_2 } \right]}} = \frac{{Np_1 \times \left[ {Np_1 p_2 ' + N\left( {1 - p_1 } \right)p_2 } \right]}}{{Np_1 p_2 ' }} \\ = N\left[ {\frac{{p_2 }}{{p_2 ' }} + p_1 \left( {1 - \frac{{p_2 }}{{p_2 ' }}} \right)} \right] \\ \end{array} \]
If the two catchabilities are equal, the ratios are all one in the last expression, and the estimator is approximately unbiased. If fish become trap shy, then the ratios are both greater than unity, and the estimator again overestimates the abundance. Intuitively, trap shyness reduces the observed number of marks below what is expected and inflates the estimated abundance.
Again, if the capture probability at the first sampling event (\(p_1\)) is small, the relative bias can be approximated by the ratio of the subsequent catchabilities.
5.4 Tag loss
Tags can be lost for a variety of reasons, e.g. breakage or tearing from the fish.
Let \(\rho\) represent the probability of retaining a tag between the two sampling occasions. Then
- \(E\left[{n_1} \right] \approx N p_1\)
- \(E\left[{n_2} \right] \approx N p_2\)
- \(E\left[ {m_2 } \right] = Np_1 \rho p_2\)
and
\[ E[\widehat{N}] \approx \frac{{E\left[ {n_1 } \right]E\left[ {n_2 } \right]}}{{E\left[ {m_2 } \right]}} = \frac{{Np_1 \times Np_2 }}{{Np_1 \rho p_2 }} = \frac{N}{\rho } \]
Intuitively, tag loss results in fewer tags being observed in the second sample than expected with a consequent positive bias in the estimated abundance. Using the rule of thumb from Cochran (1977), the bias resulting from tag loss can be “ignored” if
\[ \mathit{tag~loss~probability}= 1-\rho < \frac{0.1}{\sqrt{E[ m_T]}}\] where \(m_T\) is the number of marks actually recovered.
Tag loss can be detected by double tagging all or a fraction of the fish released (Section 10). This second tag can be a batch mark (e.g. a fin clip) or a second tag of the same or different tag material (e.g., a disc tag could be used for the second tag if the first tag was a spaghetti tag).
5.6 Homogeneity in catchablity
Variable catchability is one of the major problem in capture-recapture methods. Heterogeneity in catchability has been divided into two categories – pure heterogeneity where catchability varies among fish but the relative catchability of individual fish among themselves does not change between sampling occasions, and variable heterogeneity where the catchability of individuals varying within sampling occasions and the relative catchability of individual may vary across sampling occasions.
5.6.1 Pure heterogeneity
In pure heterogeneity, fish vary in their catchability due to random chance or related to covariates such a sex or body length. However, the relative catchability of individuals compared to other individuals remains fixed over the course of the study. For example, males may be more catchable than females, and remain more catchable in both sampling occasions. Or nets may be used to select fish, and net selectivity is related to body length which doesn’t change much between sampling occasions.
To illustrate the effects of heterogeneity, suppose that there are two sub-populations with a fraction \(a\) in the first sub-population and \(1-a\) in the second sub-population. Let \(p_1\) and \(p_2\) represent the catchability of the first subpopulation at the two sampling occasions, and suppose that the second sub-population has catchabilities \(b p_1\) and \(b p_2\) respectively. The constant \(b\) represents the differential catchability among the two sub-populations at the two sampling occasions.
Then
- \(E\left[{n_1} \right] \approx N a p_1 + N (1-a) b p_1\)
- \(E\left[{n_2} \right] \approx N a p_2 + N (1-a) b p_2\)
- \(E\left[ {m_2 } \right] = N a p_1 p_2 + N (1-a) b p_1 b p_2\)
and \[ \begin{array}{c} E\left[ {\hat N} \right] \approx \frac{{E\left[ {n_1 } \right]E\left[ {n_2 } \right]}}{{E\left[ {m_2 } \right]}} \\ = \frac{{[Nap_1 + N(1 - a)bp_1 ][Nap_2 + N(1 - a)bp_2 ]}}{{Nap_1 p_2 + N(1 - a)bp_1 bp_2 }} \\ = N\frac{{\left[ {a + b(1 - a)} \right]^2 }}{{a + b^2 (1 - a)}} < N \\ {\textrm{ }} \\ \end{array} \]
In general, pure heterogeneity leads to a negative bias in the Petersen estimator. Intuitively, the more catchable fish are caught too often which leads to an increase in the observed number of marks compared to homogeneous catchable populations and a deflation of the estimator. Indeed, if certain fractions of the population are uncatchable (e.g., \(b=0\)) then the population estimates will always EXCLUDE the uncatchable segment and estimates only \(Na\). If the second sub-population has the same catchability as the first population \(a=1\), then there is no bias (as expected).
If the heterogeneity is related to a fixed categorical covariate (such as sex), then the bias can be removed by stratifying the population by categories and performing independent estimates for each category (see Section 6).
In many cases, heterogeneity is related to a continuous covariate such a body length and induced by net selectivity. This continuous covariate can be used to model the catchability. Alternatively, Chen and Lloyd (2000) developed a non-parametric method to account for this type of heterogeneity – see Section 7.3 for details.
5.6.2 Variable heterogeneity
5.6.2.1 General heterogeneity
Both the cases above (pure heterogeneity and changing heterogeneity) can be subsumed into a general expression for the bias introduced by heterogeneity.
This can be generalized to a continuous distribution of catchabilities, say as a function of body length. Junge (1963) and Seber (1982, p. 86) show that the relative bias (\(RB=\frac{E[\widehat{N}]-N}{N}\)) can be approximated by: \[RB \approx - C \left( {p_{1j},p_{2j}} \right) \times \frac{\sqrt {V(p_{1j}) V(p_{2j}) }}{E\left[ {p_{1j} p_{2j}} \right]}\] where \(C(\cdot,\cdot)\) is the correlation of catchabilities between sampling occasions, \(V(\cdot)\) are the variability of the catchabilities at each sampling occasion, all taken over the individuals (\(j\)).
If all animals are equally catchable at either sampling occasion (e.g., a random sample at either sampling occasion), then the \(p_j\) are constant, the correlation is zero because any random variable has a 0 correlation with a constant. There is no bias.
If the catchabilities vary among individuals but the catchability in the second sample does not depend upon the catchability in the first sample, the correlation is again zero and there is no bias. This is reason for recommending that different sampling methods be used a each sampling occasion.
If the heterogeneity is related to a fish covariate such as size and the same sampling methods are used in both sampling occasions, then a positive correlation exists between the catchabilities and a negative bias in the estimate occurs.
Trap shyness leads to a negative correlation between the two capture probabilities, and a positive bias as seen earlier.
Junge(1963) and Seber(1982, p. 86) also examined how extreme the bias could be in the special case where \(p_{2j}=bp_{1j}\), i.e., pure heterogeneity among animals. In this case the correlation is 1, and the relative bias simplifies to: \[RB \approx - \frac{V(p_{1j})}{E\left[ {p_{1j}^2} \right]}\] This can be used to approximate the extent of the bias introduced by pure heterogeneity.
Expand on this here more, e.g. assume a beta distribution for p1 with various SD.
5.7 Spreadsheet to investigate impact of assumption violations
It is rare that a simple violation of assumptions will be occurring. The effect of multiple violations can be investigated using the spreadsheet supplied with this monograph.
The spreadsheet is set up to accommodate up to 4 segments of the population (e.g., strata), and has columns for the various assumption violations. The baseline condition is set up using guessestimates for the abundance and catchability probability and, as expected, no bias is seen in the estimates (Figure 6):
Now it is straight forward to investigate differences in catchability catchability and mortality between marked and unmarked fish. Suppose that marked fish are slightly less catchable at the second sampling event (\(p_2^{marked}=.016\); \(p_2^{unmarked}=.017\)) and that marked fish have a survival probability of 0.95. The resulting bias is around 17% (Figure 7):
If heterogeneity is related to a fixed attribute, such as sex, the parameter values now are entered into 2 (or more) rows of the table. For examples, suppose we have a population with a 50:50 sex ratio; females are less catchable at the first event, and more catchable at the second event. The approximate bias is around 20% (Figure 8):
Finally, if heterogeneity is associated with geographic or temporal movement, a simple example allowing for a combination of 2 tagging strata (N vs S) and 2 recapture strata (N vs S) can be examined. Here we divide the population in to 4 categories corresponding to the 4 possible pairs of movements, and specify suitable values for the catchabilities. The estimated bias is around 5% (Figure 9):
Generally speaking, two tagging x two recapture strata will be sufficient to determine the approximate size of any bias.
5.8 Empirical adjustments to existing estimates
While it is possible to obtain a corrected point estimate using the analytical analysis above, finding the SE of the adjust estimate is more complex, especially if several adjustment factors are involved.
Consequently, and empirical adjustment can be obtained using the LP_est_adjust() function that takes the estimates (and SE) of abundance and estimates of the adjustment factor (and SE) and simulates the impact of the adjustments. A log-normal distribution is assumed for the estimates of abundance, and a distribution for each individual adjustment factor is determined using the corresponding estimate and SE. Once the effects of the combined adjustments is simulated, the distribution of the abundance estimates is back-transformed and the adjusted SE (and confidence intervals) is determined. This process is analogous to what happens in a Bayesian analysis.
5.8.1 Adjusting for tag loss
5.8.1.1 Adjusting Rodli estimates for tag loss
Suppose we wish to adjust the Rodli estimates for tag loss. Recall the estimated abundance was 338 (SE 25) fish.
Suppose that the empirical estimate of tag retention is 0.90 (SE .05). The adjusted estimate is found as:
set.seed(23432)
rodli.est.mt.adjust <- LP_est_adjust(
rodli.est.mt$summary$N_hat, rodli.est.mt$summary$N_hat_SE,
tag.retention.est=0.90, tag.retention.se=0.05,
)A comparison of the original and adjusted estimates of the abundance are:
rodli.est.mt.adjust$summary N_hat_un N_hat_un_SE N_hat_adj N_hat_adj_SE N_hat_adj_LCL N_hat_adj_UCL
1 338.4737 25.49646 305.7388 28.62206 250.8642 364.0012
5.8.1.2 Example from a double tagging study
In Section 10.4.2, a double tagging study was conducted, and estimates of abundance and and the tag retention probability were obtained. We will re-analyze this data, using only 1 tag and then do the empirical adjustment (assuming we know the tag retention probability),
First we get the double tag data and remove information from the second tag (it doesn’t matter that some revised histories are duplicated).
data(data_sim_tagloss_twoD)
data_one_tag <- data_sim_tagloss_twoD
data_one_tag$old_cap_hist <- data_one_tag$cap_hist
data_one_tag$cap_hist <- paste0(substr(data_one_tag$cap_hist,1,1),
substr(data_one_tag$cap_hist,3,3))This gives the “single tag” data:
cap_hist freq old_cap_hist
1 01 879 0010
2 10 225 1000
3 11 14 1010
4 10 666 1100
5 10 21 1101
6 11 7 1110
7 11 37 1111
We now fit the regular Petersen estimator and get the estimates that are now biased because of tag loss:
data_one_tag.fit <- Petersen::LP_fit(data_one_tag, p_model=~1)
data_one_tag.est <- Petersen::LP_est(data_one_tag.fit)
data_one_tag.est$summary N_hat_f N_hat_rn N_hat N_hat_SE N_hat_conf_level N_hat_conf_method
1 ~1 (Intercept) 15675.21 1933.056 0.95 logN
N_hat_LCL N_hat_UCL p_model name_model cond.ll n.parms nobs method
1 12309.6 19961.03 ~1 p: ~1 -1499.301 1 1849 CondLik
And we make the empirical adjustment based on the results from the tag loss study:
data_one_tag.est.adj <- Petersen::LP_est_adjust(
data_one_tag.est$summary$N_hat,
data_one_tag.est$summary$N_hat_SE,
tag.retention.est=.64,
tag.retention.se =.06)giving:
data_one_tag.est.adj$summary N_hat_un N_hat_un_SE N_hat_adj N_hat_adj_SE N_hat_adj_LCL N_hat_adj_UCL
1 15675.21 1933.056 10099.55 1562.258 7339.145 13413.14
The estimate is similar to that in Section 10.4.2, but of course the SE is larger because the information from the other tags is not longer available.
5.8.2 Overlooked tags/Non-reporting of tags
Rajwani and Schwarz (1997) considered the situation where a sub-sample of fish that supposedly did not have tags is reinspected to count the number of missed tags. The data on males is taken from Rajwani and Schwarz (1997)
As fish return to their spawning sites, \(n_1=1510\) are captured using seine nets. A Petersen disk tag is attached and the fish is released. After spawning, the fish die and the carcasses are often washed onto the banks of the spawning area. Survey teams walk along the banks looking for carcasses. When a carcass is found, it is examined for a tag. After enumeration, all tags are cut from the carcasses, and those carcasses are removed from the study area by cutting them into two with a machete and returning them to the river. Untagged carcasses are left where found.
A total of \(n_2=45595\) carcasses are examined and \(m_2=279\) marks are observed. Later in the season, a second team examines some of those carcasses identified as being without tags to check for tags missed in the initial survey. A total of \(n_3=8462\) carcasses are reexamined (subsampled) and \(m_3=6\) new tags are found.
The data and capture histories are:
cap_hist freq
1 10 1231
2 11 279
3 01 45316
We start with the standard conditional-likelihood Petersen estimate:
data_overlook.fit <- Petersen::LP_fit(data_overlook, p_model=~..time)
data_overlook.est <- Petersen::LP_est(data_overlook.fit)
data_overlook.est$summary N_hat_f N_hat_rn N_hat N_hat_SE N_hat_conf_level N_hat_conf_method
1 ~1 (Intercept) 246768.4 13298.26 0.95 logN
N_hat_LCL N_hat_UCL p_model name_model cond.ll n.parms nobs method
1 222033.5 274258.7 ~..time p: ~..time -7393.831 2 46826 CondLik
This estimate is biased upwards because of the non-reporting of tags. Rajwani and Schwarz (1997) give the analytical expressions for the estimate of the reporting probability: \[\widehat{\rho} = \frac{m_2}{m_2+ n_{01}\frac{m_3}{n_3}}=\frac{279}{279+ 45316\frac{6}{8462}}\]
We estimate the uncertainty in the reporting probability empirically:
# estimate the reporting rate
rho = m2/(m2+ (n2-m2)*m3/n3)
rho.sim <- m2/(m2+ (n2-m2)*(rbeta(10000,m3,n3-m3)))
rho.se = sd(rho.sim)This gives an estimated reporting probability of 0.897 (SE 0.037).
These values are used to adjust the previous estimate
data_overlook.est.adj <- Petersen::LP_est_adjust(
data_overlook.est$summary$N_hat,
data_overlook.est$summary$N_hat_SE
,
tag.reporting.est=rho,
tag.reporting.se =rho.se)
data_overlook.est.adj$summary N_hat_un N_hat_un_SE N_hat_adj N_hat_adj_SE N_hat_adj_LCL N_hat_adj_UCL
1 246768.4 13298.26 221357.3 14977.76 192665.1 250574.5
These results are very similar to those in Rajwani and Schwarz (1997) of \(\widehat{N}\)=221,284 (SE 15,068) fish.
6 Accounting for heterogeneity I - fixed discrete strata
Heterogeneity is likely the most common reason for extensive bias in the Petersen estimator. Pure heterogeneity, i.e., some fish are always more catchable than other fish, leads to a negative bias in the estimated abundance. Heterogeneity that varies among fish and between the two sample times can lead to positive or negative bias depending upon the correlation of the heterogeneity over the animals between the two sample times.
A common way to correct for biases caused by heterogeneity is stratification where animals are separated in to groups by a measured covariate. There are four types of covariates that are commonly measured in (roughly) increasing order of complexity of analysis:
- fixed, individual categorical covariates such as sex.
- fixed, individual continuous covariates such as length in short studies.
- changing, individual, categorical covariates such as location or timing of capture at each sampling event.
- changing, individual continuous covariates such as length in long studies.
This section demonstrates the analysis of fixed, individual covariates such as sex.
6.1 Fixed individual categorical covariates such as sex
Very often a simple fixed categorical covariate is measured on individual fish such as sex at both sampling occasions. This device can also be used with continuous covariates (such as length) that do not change much over the course of a season if the continuous covariate is broken into distinct classes (e.g., length classes) as shown in Section 6.3.
A key assumption for this section is that fish do not change categories between the two sampling intervals.
6.1.1 Test for equal marked fractions
As a first step, a simple contingency table test can be used to examine if there is statistical evidence of differential catchability either in the first or second samples. Recall that the estimated catchabilities are found as \(\widehat{p}_1 = \frac{m_2}{n_2}\) and \(\widehat{p}_2 = \frac{m_2}{n_1}\). So, if there are \(K\) classes, a contingency table to test the equality of catchability at the first sample is equivalent to the test of presence of recruitment among groups found in Table 5 and is a test of equal marked fractions across the strata.
The usual \(\chi^2\) statistic is computed and is used to test if the marked fraction (the catchability at time \(1\)), are equal across all strata. If the hypothesis is rejected , then this MAY be evidence of differential catchability at time \(1\).
6.1.2 Test for equal catchability
Similarly, the contingency table found in Table 4 can be used to test if the recapture probabilities at the second sampling occasion are equal.
6.1.3 Stratifed models
If there is evidence that catchabilities may differ among the strata at least one sampling occasion, the simplest strategy is to compute separate Petersen estimates for each stratum and then combine the estimates. For example, if the population is stratified by sex and no assumption is made about the sex ratio at each sampling occasion, nor about equality of catchability at the sampling occasions, application of the previous methods lead to two estimates of abundance, one for each sex, and their associated standard error.
The combined estimate of abundance is found as: \[\widehat{N}_{combined}= \widehat{N}_f + \widehat{N}_m\] and the \(SE\) of the combined estimator is found as: \[se(\widehat{N}_{combined})= \sqrt{se(\widehat{N}_f)^2 + se(\widehat{N}_m)^2}\] The extension to more than two categories is straightforward.
However, this strategy could be inefficient, if the catchability differs among the strata only at a single sampling occasion. For example, the catchability of both sexes may be the same at sample time \(1\), but differ at sample time \(2\).
There are four possible general models that could be fit. There are also several possible models where only some of the strata have equal catchability at either/both of the sampling occasions. The general theory presented here will also accommodate these cases.
- Complete homogeneity: \(p_{1A}=p_{1B}=\ldots=p_{1K}\) and \(p_{2A}=p_{2B}=\ldots=p_{2K}\).
- Homogeneity at time 1 only: Only \(p_{1A}=p_{1B}=\ldots=p_{1K}\).
- Homogeneity at time 2 only: Only \(p_{2A}=p_{2B}=\ldots=p_{2K}\).
- Complete heterogeneity: No equality at either sampling occasion.
The Akiake Information Criterion (AIC; Akaike, 1973) paradigm is a preferred method of dealing with multiple models for the same data. Burnham and Anderson (2002) provides a detailed reference on the use of this methodology. In brief, this paradigm asserts that none of the models fit to data are the “truth” (do you really believe that all individual of the same sex have exactly the same catchability). Rather all models are approximation to reality and several models may approximate reality almost equally well. The AIC statistic is computed for each model and is a measure of fit and a penalty for the number of parameters used to fit the model. The AIC statistic can be used to derive model weights which are a measure of relative strength in explaining the data among the competing models. A weighted average of the estimates from the competing model can be computed and the \(SE\) of this estimate can incorporate both the individual precision from each of the model plus a measure of model uncertainty. For example, if the various models give vastly different estimates of the population abundance, then the model uncertainty about the population abundance will be large. Conversely, if the various models agree to a great extent in their estimate, then the uncertainty in the estimate due to model choice is small.
In some cases, additional information can, and should be used to improve precision. For example, in many species, the sex ratio in the population is known from other surveys or is assumed to be 50:50. I am unaware of any previous work on incorporating knowledge of the the stratum population ratios into the estimation framework.
6.2 Example: Northern Pike - simple stratification
In 2005, the Minnesota Department of Natural Resources conducted a tagging study to estimate the number of northern pike (Esox lucius) in Mille Lacs, Minnesota. Briefly, approximately 7,000 fish were sexed and tagged on their spawning grounds in the spring and a summer gillnet assessment captured about 1,000 fish. Complete details are in Bruesewitz and Reeves (2005).
Fish were double tagged, but an analysis using a tag-retention model showed that tag loss was negligible (Section 10.6).
Each fish has its own individual history. The sex and length (inches) of the fish at the time of capture are also recorded. The first few records are:
data(data_NorthernPike)
head(data_NorthernPike)
## cap_hist length Sex freq
## 1 01 23.20 M 1
## 2 01 28.89 F 1
## 3 01 25.20 M 1
## 4 01 22.20 M 1
## 5 01 25.00 M 1
## 6 01 24.70 M 16.2.1 Summary statistics by sex
The summary statistics by sex are found in Table 6.
Sex | n1 | n2 | m2 | P(recapture) | Marked fraction |
|---|---|---|---|---|---|
F | 4,045 | 613 | 89 | 0.022 | 0.145 |
M | 2,777 | 527 | 68 | 0.024 | 0.129 |
ALL | 6,822 | 1,140 | 157 | 0.023 | 0.138 |
The recapture probabilities are similar across the two sexes as are the marked fractions. However, with a large sample size, small differences in capture probabilities may be detected.
The analysis will be done using the capture histores for individual fish, but you can construct the capture histories from the summary statistics as shown below:
cap_hist <- n1_n2_m2_to_cap_hist(n1=c(4045,2777),
n2=c(613,527),
m2=c(89,68),
strata=c("F","M"),stratum_var="Sex")
cap_hist cap_hist freq Sex
1 10 3956 F
2 10 2709 M
3 01 524 F
4 01 459 M
5 11 89 F
6 11 68 M
6.2.2 Test for equal marked fractions by sex
The contingency table to test for equal catchability at sampling occasion 1 (indicated by the marked fraction seen at the second occasion) is computed using the LP_test_equal_mf() function to test for equal marked fractions:
nop.equal.mf.sex <- LP_test_equal_mf(data_NorthernPike, "Sex") This gives the summary table in Table 7.
Number of fish | Proportions | |||
|---|---|---|---|---|
status | F | M | F | M |
Not seen at t1 | 524 | 459 | 0.855 | 0.871 |
Recaptured | 89 | 68 | 0.145 | 0.129 |
and the resulting chi-square test output is:
##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: tab
## X-squared = 0.4942, df = 1, p-value = 0.4821
The \(\chi^2\) test \(p\)-value for equal marked fraction is p = 0.482 and so there is no evidence of differential marked fractions.
6.2.3 Test for equal recapture probabilities by sex
The contingency table to test for equal recapture probability from fish tagged at sampling occasion 1 is computed using the LP_test_equal_recap() function:
nop.equal.recap.sex <- LP_test_equal_recap(data_NorthernPike, "Sex") This gives the summary table in Table 8.
Number of fish | Proportions | |||
|---|---|---|---|---|
status | F | M | F | M |
Never seen | 3,956 | 2,709 | 0.978 | 0.976 |
Recaptured | 89 | 68 | 0.022 | 0.024 |
and the results of the \(\chi^2\) test are:
##
## Pearson's Chi-squared test with Yates' continuity correction
##
## data: tab
## X-squared = 0.34826, df = 1, p-value = 0.5551
The \(p\)-value for equal recapture probability is p = 0.555 and so there is no evidence of differential recapture probabilities between the two sexes.
6.2.4 Fitting multiple models by sex
While these two tests indicate no evidence of differential catchability at either sampling occasion, they do not necessarily indicate that the two sexes can be completely pooled when computing the Petersen estimates.
Several models can be fit to the NorthernPike data:
- Completely pooled Petersen. Capture-probabilities at each sampling event do not depend on Sex. This is equivalent to fitting a simple Petersen model ignoring sex.
- Completely stratified-Petersen. Capture-probabilities at each sampling event depend on Sex. This is equivalent to fitting two separate Petersen models, one for each sex.
- Pure heterogeneous models where the probability of capture varies between the two sexes, but is consistently the same across sampling events. This is equivalent to an additive model between sex and time.
These models were fit to the northern pike data:
data(data_NorthernPike)
# Fit the various models
nop.fit.time <- Petersen::LP_fit(data_NorthernPike, p_model=~..time)
nop.fit.sex.time <- Petersen::LP_fit(data_NorthernPike, p_model=~-1+Sex:..time)
nop.fit.sex.p.time <- Petersen::LP_fit(data_NorthernPike, p_model=~Sex+..time)
# Fit models where the p(capture) is equal at t1 or t2 but not both.
# This is intermediate between the ~..time and ~..time:Sex models
nop.fit.eq.t1 <- Petersen::LP_fit(data_NorthernPike,
p_model=~-1+I(as.numeric(..time==1))+
I(as.numeric(..time==2)):Sex)
nop.fit.eq.t2 <- Petersen::LP_fit(data_NorthernPike,
p_model=~-1+I(as.numeric(..time==2))+
I(as.numeric(..time==1)):Sex)Notice the formula for the p_model to force the capture-probabilities to be equal at the first or second sampling event and to vary by sex for the other sampling event. The I() notation in the model formula indicates that the interior expression is to evaluated first before being using in the model. In this case, we create an indicator variable if the sampling event is the first or second event.
We can now rank these models in terms of AICc (Table 9):
# compare the various models
nop.sex.aictab <- LP_AICc(
nop.fit.time,
nop.fit.sex.time,
nop.fit.sex.p.time,
nop.fit.eq.t1,
nop.fit.eq.t2) Model specification | Conditional log-likelihood | # parms | # obs | AICc | Delta | AICcWt |
|---|---|---|---|---|---|---|
p: ~-1 + I(as.numeric(..time == 2)) + I(as.numeric(..time == 1)):Sex | -3,696.051 | 3 | 7,805 | 7,398.11 | 0.00 | 0.42 |
p: ~-1 + I(as.numeric(..time == 1)) + I(as.numeric(..time == 2)):Sex | -3,696.139 | 3 | 7,805 | 7,398.28 | 0.18 | 0.38 |
p: ~-1 + Sex:..time | -3,695.826 | 4 | 7,805 | 7,399.66 | 1.55 | 0.19 |
p: ~..time | -3,702.341 | 2 | 7,805 | 7,408.68 | 10.58 | 0.00 |
p: ~Sex + ..time | -3,702.228 | 3 | 7,805 | 7,410.46 | 12.35 | 0.00 |
The AIC weight indicate high support for either model where the capture probabilities are equal either at the first or the second but not both sampling occasions. The model that involves complete pooling over both sexes (pooled Petersen) is given a very low weight (less than 1%). The model that has completely separate estimates for males and females is given a lower weight (only about 19%) as well.
We can now extract the estimates of the overall abundance from the models and obtain the model averaged values as shown in Table 10:
# extract the estimates of the overall abundance
nop.sex.ma.N_hat_all<- LP_modavg(
nop.fit.time,
nop.fit.sex.time,
nop.fit.sex.p.time,
nop.fit.eq.t1,
nop.fit.eq.t2, N_hat=~1) N_hat_f | N_hat_rn | Modnames | AICcWt | Estimate | SE |
|---|---|---|---|---|---|
~1 | (Intercept) | p: ~-1 + I(as.numeric(..time == 2)) + I(as.numeric(..time == 1)):Sex | 0.42 | 49,536 | 3,629 |
~1 | (Intercept) | p: ~-1 + I(as.numeric(..time == 1)) + I(as.numeric(..time == 2)):Sex | 0.38 | 49,536 | 3,629 |
~1 | (Intercept) | p: ~-1 + Sex:..time | 0.19 | 49,382 | 3,616 |
~1 | (Intercept) | p: ~..time | 0.00 | 49,536 | 3,629 |
~1 | (Intercept) | p: ~Sex + ..time | 0.00 | 49,596 | 3,643 |
Model averaged | 49,506 | 3,627 |
Notice that the estimates (and SE) for three of the models are identical – the pooled Petersen estimator (4th model), and the two model where the capture-probabilities are the same at either sampling event. The latter two models are one of the cases where the pooled-Petersen is unbiased, i.e., the capture-probabilities are homogeneous at either of the sampling events.
If only the model where each sex is modeled independently was used, the estimated abundances would have been 49,382 ( \(SE\) 3,616) fish. In the models where the effect of sex was ignored either completely or at either of the sampling occasions, the estimated abundance would have been 49,536 ( \(SE\) 3,629) fish. In this case, this extra work in trying to model the catchabilities did not lead to estimates that were very different than this most general model.
So what is the advantage of the first two models vs. the pooled-Petersen. It is now possible to obtain estimates of the abundance of the two sub-populations. In the traditional pooled-Petersen estimator, it is not easy to get estimates of the sub-population, but this can also be done using the conditional likelihood approach followed by the Horvitz-Thompson estimator (Table 11).
# extract the estimates of the abundance for each sex
nop.sex.ma.N_hat_sex<- LP_modavg(
nop.fit.time,
nop.fit.sex.time,
nop.fit.sex.p.time,
nop.fit.eq.t1,
nop.fit.eq.t2, N_hat=~-1+Sex) N_hat_f | N_hat_rn | Modnames | AICcWt | Estimate | SE |
|---|---|---|---|---|---|
~-1 + Sex | SexF | p: ~-1 + I(as.numeric(..time == 2)) + I(as.numeric(..time == 1)):Sex | 0.42 | 26,814 | 2,048 |
~-1 + Sex | SexF | p: ~-1 + I(as.numeric(..time == 1)) + I(as.numeric(..time == 2)):Sex | 0.38 | 29,338 | 2,171 |
~-1 + Sex | SexF | p: ~-1 + Sex:..time | 0.19 | 27,860 | 2,700 |
~-1 + Sex | SexF | p: ~..time | 0.00 | 28,998 | 2,139 |
~-1 + Sex | SexF | p: ~Sex + ..time | 0.00 | 29,828 | 2,859 |
Model averaged | 27,993 | 2,506 | |||
~-1 + Sex | SexM | p: ~-1 + I(as.numeric(..time == 2)) + I(as.numeric(..time == 1)):Sex | 0.42 | 22,722 | 1,823 |
~-1 + Sex | SexM | p: ~-1 + I(as.numeric(..time == 1)) + I(as.numeric(..time == 2)):Sex | 0.38 | 20,197 | 1,499 |
~-1 + Sex | SexM | p: ~-1 + Sex:..time | 0.19 | 21,522 | 2,406 |
~-1 + Sex | SexM | p: ~..time | 0.00 | 20,538 | 1,526 |
~-1 + Sex | SexM | p: ~Sex + ..time | 0.00 | 19,768 | 2,135 |
Model averaged | 21,513 | 2,160 |
Notice how estimates of abundance are requested for each sex. Now the estimates of the sub-population abundances differ among the models even though the estimates overall population abundances are equal
6.3 Example: Northern pike stratified by length class
We return to the Northern Pike example. The length of the fish was also measured and the sampling events are close enough that the change in length between the two sampling events is negligible.
6.3.1 Distribution of length in captured fish
A histogram of the distribution of length in the handled fish is show in Figure 10.
It appears that female fish tend to be larger than male fish.
6.3.2 Summary statistics by length class
We start by classifying the length into length classes of 0:20 in, 20:25 in, 25:30 in, 30:35 in; and 35+ in. Summary statistics are presented in @bl-nop-lengthclass-sumstat
length.class | n1 | n2 | m2 | P(recapture) | Marked fraction |
|---|---|---|---|---|---|
00-20 | 569 | 22 | 1 | 0.002 | 0.045 |
20-25 | 2,238 | 371 | 41 | 0.018 | 0.111 |
25-30 | 2,120 | 537 | 86 | 0.041 | 0.160 |
30-35 | 1,254 | 173 | 25 | 0.020 | 0.145 |
35+ | 641 | 37 | 4 | 0.006 | 0.108 |
ALL | 6,822 | 1,140 | 157 | 0.023 | 0.138 |
There appears to differences in recaptured probability by length class peaking around the 25-30 inch class, but the marked-fractions appear to be similar. Notice the small number of recaptures in the first and last length classes – these strata likely should be pooled with the other strata if a fully-stratified model is used to avoid the small sample biases.
6.3.3 Test for equal marked fractions by length class
The contingency table to test for equal catchability at sampling occasion 1 (indicated by the marked fraction seen at the second occasion) is constructed as illustrated in Table 13.
nop.equal.mf.length.class <- LP_test_equal_mf(data_NorthernPike,
"length.class") Number of fish | Proportions | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
status | 00-20 | 20-25 | 25-30 | 30-35 | 35+ | 00-20 | 20-25 | 25-30 | 30-35 | 35+ |
Not seen at t1 | 21 | 330 | 451 | 148 | 33 | 0.955 | 0.889 | 0.840 | 0.855 | 0.892 |
Recaptured | 1 | 41 | 86 | 25 | 4 | 0.045 | 0.111 | 0.160 | 0.145 | 0.108 |
and the resulting chi-square test output is:
##
## Pearson's Chi-squared test
##
## data: tab
## X-squared = 6.505, df = 4, p-value = 0.1645
The \(p\)-value for equal marked fraction is p = 0.164 and so there is no evidence of differential marked fractions among the length classes.
6.3.4 Test for equal recapture probabilities by length class
The contingency table to test for equal recapture probability from fish tagged at sampling occasion 1 is constructed as illustrated in Table 14.
nop.equal.recap.length.class <- LP_test_equal_recap(data_NorthernPike,
"length.class") Number of fish | Proportions | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
status | 00-20 | 20-25 | 25-30 | 30-35 | 35+ | 00-20 | 20-25 | 25-30 | 30-35 | 35+ |
Not recaptured | 568 | 2,197 | 2,034 | 1,229 | 637 | 0.998 | 0.982 | 0.959 | 0.980 | 0.994 |
Recaptured | 1 | 41 | 86 | 25 | 4 | 0.002 | 0.018 | 0.041 | 0.020 | 0.006 |
and the resulting chi-square test output is:
##
## Pearson's Chi-squared test
##
## data: tab
## X-squared = 51.225, df = 4, p-value = 2.003e-10
The \(p\)-value for equal recapture probability is p < .001 and so there appears to be good evidence of differential recapture probabilities among the length classes. However, some of the counts in some cells are quite small and so the p-value may be too small and a Fisher Exact test may be preferable.
##
## Fisher's Exact Test for Count Data with simulated p-value (based on
## 2000 replicates)
##
## data: tab
## p-value = 0.0004998
## alternative hypothesis: two.sided
The \(p\)-value is also small, so there is evidence of a difference in the recapture probabilities by length class.
6.3.5 Fitting multiple models by length class
We fit the suite of models similar to those when stratifying by sex as shown in Table 15.
# Fit the various models
nop.fit.time <- Petersen::LP_fit(data_NorthernPike,
p_model=~-1+..time)
nop.fit.length.class.time <- Petersen::LP_fit(data_NorthernPike,
p_model=~-1+length.class:..time)
nop.fit.length.class.p.time <- Petersen::LP_fit(data_NorthernPike,
p_model=~length.class+..time)
# Fit models where the p(capture) is equal at t1 or t2 but not both.
# This is intermediate between the ~..time and ~..time:Sex models
nop.fit.eq.t1 <- Petersen::LP_fit(data_NorthernPike,
p_model=~-1+I(as.numeric(..time==1))+
I(as.numeric(..time==2)):length.class)
nop.fit.eq.t2 <- Petersen::LP_fit(data_NorthernPike,
p_model=~-1+I(as.numeric(..time==2))+
I(as.numeric(..time==1)):length.class)We can now rank these models in terms of AICc (Table 15):
# compare the various models
nop.sex.aictab <- LP_AICc(
nop.fit.time,
nop.fit.length.class.time,
nop.fit.length.class.p.time,
nop.fit.eq.t1,
nop.fit.eq.t2
) Model specification | Conditional log-likelihood | # parms | # obs | AICc | Delta | AICcWt |
|---|---|---|---|---|---|---|
p: ~-1 + I(as.numeric(..time == 1)) + I(as.numeric(..time == 2)):length.class | -3,596.138 | 6 | 7,805 | 7,204.29 | 0.00 | 0.62 |
p: ~-1 + length.class:..time | -3,592.615 | 10 | 7,805 | 7,205.26 | 0.97 | 0.38 |
p: ~-1 + I(as.numeric(..time == 2)) + I(as.numeric(..time == 1)):length.class | -3,621.220 | 6 | 7,805 | 7,254.45 | 50.16 | 0.00 |
p: ~length.class + ..time | -3,678.014 | 6 | 7,805 | 7,368.04 | 163.75 | 0.00 |
p: ~-1 + ..time | -3,702.341 | 2 | 7,805 | 7,408.68 | 204.40 | 0.00 |
The AIC weight indicate high support for either model where the capture probabilities are equal at the first sampling event (equal marked fraction) and secondarily, to a model with full stratification at both sampling events.
We can now extract the estimates of the overall abundance from the models and obtain the model averaged values as shown in Table 16:
# extract the estimates of the overall abundance
nop.length.class.ma.N_hat_all<- LP_modavg(
nop.fit.time,
nop.fit.length.class.time,
nop.fit.length.class.p.time,
nop.fit.eq.t1,
nop.fit.eq.t2, N_hat=~1) N_hat_f | N_hat_rn | Modnames | AICcWt | Estimate | SE |
|---|---|---|---|---|---|
~1 | (Intercept) | p: ~-1 + I(as.numeric(..time == 1)) + I(as.numeric(..time == 2)):length.class | 0.62 | 49,536 | 3,629 |
~1 | (Intercept) | p: ~-1 + length.class:..time | 0.38 | 60,614 | 13,039 |
~1 | (Intercept) | p: ~-1 + I(as.numeric(..time == 2)) + I(as.numeric(..time == 1)):length.class | 0.00 | 49,536 | 3,629 |
~1 | (Intercept) | p: ~length.class + ..time | 0.00 | 93,218 | 39,716 |
~1 | (Intercept) | p: ~-1 + ..time | 0.00 | 49,536 | 3,629 |
Model averaged | 53,754 | 10,091 |
Notice that the estimates (and SE) for three of the models are identical – the pooled Petersen estimator, and the two model where the capture-probabilities are the same at either sampling event. The latter two models are one of the cases where the pooled-Petersen is unbiased, i.e., the capture-probabilities are homogeneous at either of the sampling events. However, there really is only support for the model with equal capture probability at the first sampling event.
Notice that the estimate for the fully stratified Petersen is quite large but with a very large standard error. This is likely an artefact of the small number of recaptures. It is left as an exercise for the reader to refit the models, pooling the first and last length classes with the second or second-to-last classes to avoid the small sample bias problem.
Finally, here are the estimates of abundance by length class using the the Horvitz-Thompson estimator (Table 17).
# extract the estimates of the abundance for each sex
nop.length.class.ma.N_hat_length.class<- LP_modavg(
nop.fit.time,
nop.fit.length.class.time,
nop.fit.length.class.p.time,
nop.fit.eq.t1,
nop.fit.eq.t2, N_hat=~-1+length.class) N_hat_rn | Modnames | AICcWt | Estimate | SE |
|---|---|---|---|---|
length.class00-20 | p: ~-1 + I(as.numeric(..time == 1)) + I(as.numeric(..time == 2)):length.class | 0.62 | 4,146 | 345 |
length.class00-20 | p: ~-1 + length.class:..time | 0.38 | 12,518 | 12,220 |
length.class00-20 | p: ~-1 + I(as.numeric(..time == 2)) + I(as.numeric(..time == 1)):length.class | 0.00 | 1,481 | 210 |
length.class00-20 | p: ~length.class + ..time | 0.00 | 39,449 | 39,004 |
length.class00-20 | p: ~-1 + ..time | 0.00 | 3,745 | 306 |
Model averaged | 7,334 | 8,571 | ||
length.class20-25 | p: ~-1 + I(as.numeric(..time == 1)) + I(as.numeric(..time == 2)):length.class | 0.62 | 16,324 | 1,224 |
length.class20-25 | p: ~-1 + length.class:..time | 0.38 | 20,251 | 2,955 |
length.class20-25 | p: ~-1 + I(as.numeric(..time == 2)) + I(as.numeric(..time == 1)):length.class | 0.00 | 16,577 | 1,374 |
length.class20-25 | p: ~length.class + ..time | 0.00 | 20,014 | 2,849 |
length.class20-25 | p: ~-1 + ..time | 0.00 | 16,298 | 1,218 |
Model averaged | 17,819 | 2,809 | ||
length.class25-30 | p: ~-1 + I(as.numeric(..time == 1)) + I(as.numeric(..time == 2)):length.class | 0.62 | 15,306 | 1,136 |
length.class25-30 | p: ~-1 + length.class:..time | 0.38 | 13,238 | 1,281 |
length.class25-30 | p: ~-1 + I(as.numeric(..time == 2)) + I(as.numeric(..time == 1)):length.class | 0.00 | 21,717 | 1,795 |
length.class25-30 | p: ~length.class + ..time | 0.00 | 10,614 | 952 |
length.class25-30 | p: ~-1 + ..time | 0.00 | 16,317 | 1,219 |
Model averaged | 14,519 | 1,560 | ||
length.class30-35 | p: ~-1 + I(as.numeric(..time == 1)) + I(as.numeric(..time == 2)):length.class | 0.62 | 9,097 | 702 |
length.class30-35 | p: ~-1 + length.class:..time | 0.38 | 8,678 | 1,589 |
length.class30-35 | p: ~-1 + I(as.numeric(..time == 2)) + I(as.numeric(..time == 1)):length.class | 0.00 | 7,685 | 728 |
length.class30-35 | p: ~length.class + ..time | 0.00 | 9,897 | 1,775 |
length.class30-35 | p: ~-1 + ..time | 0.00 | 8,898 | 681 |
Model averaged | 8,937 | 1,144 | ||
length.class35+ | p: ~-1 + I(as.numeric(..time == 1)) + I(as.numeric(..time == 2)):length.class | 0.62 | 4,662 | 383 |
length.class35+ | p: ~-1 + length.class:..time | 0.38 | 5,929 | 2,791 |
length.class35+ | p: ~-1 + I(as.numeric(..time == 2)) + I(as.numeric(..time == 1)):length.class | 0.00 | 2,075 | 271 |
length.class35+ | p: ~length.class + ..time | 0.00 | 13,244 | 6,369 |
length.class35+ | p: ~-1 + ..time | 0.00 | 4,278 | 345 |
Model averaged | 5,145 | 1,853 |
Notice how estimates of abundance are requested for each length class. Now the estimates of the sub-population abundances differ among the models even though the estimates overall population abundances are equal
7 Accounting for heterogeneity II - continuous fixed covariate
In the previous sections, we showed how a continuous covariate could be broken into a set of discrete classes and a stratified model applied. In some cases, it may be of interest to use a smooth function of the covariates (e.g., a quadratic curve, or a spline fit) to represent, for example, the catchability curve as a function of length.
This is relatively straight forward except for a few items that need to be addressed
- Standardizing the covariates to have a mean close to 0 and a standard deviation close to 1 improves numerical stability and convergence, especially when fitting a quadratic curve.
- Animals with a very low estimated catchability have a very large expansion factor when the Horvitz-Thompson estimator is formed. You may need to remove fish with very large expansion factors when estimating abundance.
7.1 Quadratic relationship between the probability of capture and length - Northern Pike
We again return to the Northern Pike example. We first standardize the length measurement (the ls variable in the revised data frame):
data(data_NorthernPike)
data_NorthernPike$ls <- scale(data_NorthernPike$length)
head(data_NorthernPike)
## cap_hist length Sex freq ls
## 1 01 23.20 M 1 -0.7146489
## 2 01 28.89 F 1 0.3710705
## 3 01 25.20 M 1 -0.3330252
## 4 01 22.20 M 1 -0.9054607
## 5 01 25.00 M 1 -0.3711876
## 6 01 24.70 M 1 -0.4284311Now we fit several models and compare them to the previous models.
- a single quadratic curve (on the logit scale) with an additive sift between sampling events
- two separate quadratic curves (on the logit scale) for each sampling event
nop.fit.length.quad1 <- Petersen::LP_fit(data_NorthernPike,
p_model=~..time + ls + I(ls*2))
nop.fit.length.quad2 <- Petersen::LP_fit(data_NorthernPike,
p_model=~..time + ls + I(ls^2) +
..time:ls + ..time:I(ls^2))We can compare models with the previous models using length classes using the usual AICc methods (Table 18).
# compare the various models
nop.sex.aictab <- LP_AICc(
nop.fit.time,
nop.fit.length.class.time,
nop.fit.length.class.p.time,
nop.fit.eq.t1,
nop.fit.eq.t2,
nop.fit.length.quad1,
nop.fit.length.quad2) Model specification | Conditional log-likelihood | # parms | # obs | AICc | Delta | AICcWt |
|---|---|---|---|---|---|---|
p: ~..time + ls + I(ls^2) + ..time:ls + ..time:I(ls^2) | -3,575.331 | 6 | 7,805 | 7,162.67 | 0.00 | 1.00 |
p: ~-1 + I(as.numeric(..time == 1)) + I(as.numeric(..time == 2)):length.class | -3,596.138 | 6 | 7,805 | 7,204.29 | 41.61 | 0.00 |
p: ~-1 + length.class:..time | -3,592.615 | 10 | 7,805 | 7,205.26 | 42.59 | 0.00 |
p: ~-1 + I(as.numeric(..time == 2)) + I(as.numeric(..time == 1)):length.class | -3,621.220 | 6 | 7,805 | 7,254.45 | 91.78 | 0.00 |
p: ~length.class + ..time | -3,678.014 | 6 | 7,805 | 7,368.04 | 205.37 | 0.00 |
p: ~-1 + ..time | -3,702.341 | 2 | 7,805 | 7,408.68 | 246.01 | 0.00 |
p: ~..time + ls + I(ls * 2) | -3,702.290 | 4 | 7,805 | 7,412.59 | 249.91 | 0.00 |
The model with two separate quadratic fits is by far the best fitting model.
We obtain the estimate of abundance and look at the estimated relationship between the length and the probability of capture (Figure 11)
nop.est.length.quad2 <- Petersen::LP_est(nop.fit.length.quad2, N_hat=~1)
est.p <- nop.est.length.quad2$detail$data.expand
ggplot(data=est.p, aes(x=length, y=p, color=as.factor(..time)))+
geom_point()+
geom_line(size=.1)+
scale_color_discrete(name="Sample\nevent")+
xlab("Length (in)")+
ylab("Estimated p(capture)")We see that the relationship at time 1 is quite peaked but not so much for sampling event 2 which is in accordance to the results from classifying length into discrete bins.
This model also shows a positive association between catchability at the two sampling events (Figure 12)
est.p <- nop.est.length.quad2$detail$data.expand
temp <- tidyr::pivot_wider(est.p,
id_cols=c("..index", "length"),
values_from="p",
names_from="..time",
names_prefix="t")
ggplot(data=temp, aes(x=t1, y=t2, color=length))+
geom_point()+
scale_color_continuous(name="Length")+
xlab("Estimated p(capture) at sample event 1")+
ylab("Estimated p(capture) at sample event 2")The odd shape to the relationship is an artefact of the quadratic curves where the top/bottom half of the “curve” correspond to the ascending/descending limbs of the quadratic curve seen in Figure 11.
Figure 12 implies a positive correlation between the two capture probabilities which implies that the pooled-Petersen estimator will have a negative bias as seen in the model averaged results (Table 20).
The estimated abundance from the best fitting model is:
nop.est.length.quad2$summary
## N_hat_f N_hat_rn N_hat N_hat_SE N_hat_conf_level N_hat_conf_method
## 1 ~1 (Intercept) 59209.91 9365.551 0.95 logN
## N_hat_LCL N_hat_UCL p_model
## 1 43426.54 80729.73 ~..time + ls + I(ls^2) + ..time:ls + ..time:I(ls^2)
## name_model cond.ll n.parms nobs
## 1 p: ~..time + ls + I(ls^2) + ..time:ls + ..time:I(ls^2) -3575.331 6 7805
## method
## 1 CondLikThe estimate appears on the large side with a large standard error compared to the other estimates seen previously. We suspect that some histories have a very small probability of capture and a large expansion factor as shown in Figure 13
est.ef <- nop.est.length.quad2$detail$data
ggplot(data=est.ef, aes(x=length, y=..EF))+
geom_point()+
geom_line()+
xlab("Length (in)")+
ylab("Estimated expansion factor")We can see that there are several large fish with expansion factors that appear to be much larger than the majority of fish. We can estimate the abundance truncating the expansion factor, say at 30:
nop.est.length.quad2.tef <- Petersen::LP_est(nop.fit.length.quad2,
N_hat=~-1+I(as.numeric(..EF<30)))
plyr::rbind.fill(nop.est.length.quad2 $summary,
nop.est.length.quad2.tef$summary)
## N_hat_f N_hat_rn N_hat N_hat_SE
## 1 ~1 (Intercept) 59209.91 9365.551
## 2 ~-1 + I(as.numeric(..EF < 30)) I(as.numeric(..EF < 30)) 58866.46 9005.852
## N_hat_conf_level N_hat_conf_method N_hat_LCL N_hat_UCL
## 1 0.95 logN 43426.54 80729.73
## 2 0.95 logN 43615.86 79449.54
## p_model
## 1 ~..time + ls + I(ls^2) + ..time:ls + ..time:I(ls^2)
## 2 ~..time + ls + I(ls^2) + ..time:ls + ..time:I(ls^2)
## name_model cond.ll n.parms nobs
## 1 p: ~..time + ls + I(ls^2) + ..time:ls + ..time:I(ls^2) -3575.331 6 7805
## 2 p: ~..time + ls + I(ls^2) + ..time:ls + ..time:I(ls^2) -3575.331 6 7805
## method
## 1 CondLik
## 2 CondLikNotice the use of the special variable ..EF in the model for N_hat. The estimate is reduced (as expected) but not by a great extent, so there is no real reason to adopt this second estimate.
Finally, we can again do the model averaging (Table 20):
# extract the estimates of the abundance
nop.length.class.ma.N_hat_length.class<- LP_modavg(
nop.fit.time,
nop.fit.length.class.time,
nop.fit.length.class.p.time,
nop.fit.eq.t1,
nop.fit.eq.t2,
nop.fit.length.quad1,
nop.fit.length.quad2, N_hat=~1) Modnames | AICcWt | Estimate | SE |
|---|---|---|---|
p: ~..time + ls + I(ls^2) + ..time:ls + ..time:I(ls^2) | 1.00 | 59,210 | 9,366 |
p: ~-1 + I(as.numeric(..time == 1)) + I(as.numeric(..time == 2)):length.class | 0.00 | 49,536 | 3,629 |
p: ~-1 + length.class:..time | 0.00 | 60,614 | 13,039 |
p: ~-1 + I(as.numeric(..time == 2)) + I(as.numeric(..time == 1)):length.class | 0.00 | 49,536 | 3,629 |
p: ~length.class + ..time | 0.00 | 93,218 | 39,716 |
p: ~-1 + ..time | 0.00 | 49,536 | 3,629 |
p: ~..time + ls + I(ls * 2) | 0.00 | 49,563 | 3,635 |
Model averaged | 59,210 | 9,366 |
The quadratic model is so much a better fit that it overwhelms the other models and the model averaged estimate is basically the first model. Notice that the model averaged confidence interval is larger than the original model because the variation in estimates among the models has also been taken into account.
It would be interesting to fit quadratic on log(length) to give a skewed catchability curve.
7.2 Spline relationship between the probability of capture and length - Northern Pike
The quadratic curve fairly ridged in its shape. An alternate way to fit a curve to the catchabilities is through the use of splines.
Give a tutorial on splines here and how to choose the appropriate values for df etc - use AIC to select
We continue with the Northern Pike example and fit a model with a separate spline curve at each sample event.
nop.fit.length.sp2.df4<- Petersen::LP_fit(data_NorthernPike,
p_model=~..time+bs(ls, df=4) +
..time:bs(ls, df=4))
nop.fit.length.sp2.df5<- Petersen::LP_fit(data_NorthernPike,
p_model=~..time+bs(ls, df=5) +
..time:bs(ls, df=5))We can compare models using the usual AICc methods (Table 21).
# compare the various models
nop.sex.aictab <- LP_AICc(
nop.fit.time,
nop.fit.length.class.time,
nop.fit.length.class.p.time,
nop.fit.eq.t1,
nop.fit.eq.t2,
nop.fit.length.quad1,
nop.fit.length.quad2,
nop.fit.length.sp2.df4, nop.fit.length.sp2.df5) Model specification | Conditional log-likelihood | # parms | # obs | AICc | Delta | AICcWt |
|---|---|---|---|---|---|---|
p: ~..time + bs(ls, df = 4) + ..time:bs(ls, df = 4) | -3,565.507 | 10 | 7,805 | 7,151.04 | 0.00 | 0.85 |
p: ~..time + bs(ls, df = 5) + ..time:bs(ls, df = 5) | -3,565.290 | 12 | 7,805 | 7,154.62 | 3.58 | 0.14 |
p: ~..time + ls + I(ls^2) + ..time:ls + ..time:I(ls^2) | -3,575.331 | 6 | 7,805 | 7,162.67 | 11.63 | 0.00 |
p: ~-1 + I(as.numeric(..time == 1)) + I(as.numeric(..time == 2)):length.class | -3,596.138 | 6 | 7,805 | 7,204.29 | 53.24 | 0.00 |
p: ~-1 + length.class:..time | -3,592.615 | 10 | 7,805 | 7,205.26 | 54.22 | 0.00 |
p: ~-1 + I(as.numeric(..time == 2)) + I(as.numeric(..time == 1)):length.class | -3,621.220 | 6 | 7,805 | 7,254.45 | 103.41 | 0.00 |
p: ~length.class + ..time | -3,678.014 | 6 | 7,805 | 7,368.04 | 217.00 | 0.00 |
p: ~-1 + ..time | -3,702.341 | 2 | 7,805 | 7,408.68 | 257.64 | 0.00 |
p: ~..time + ls + I(ls * 2) | -3,702.290 | 4 | 7,805 | 7,412.59 | 261.54 | 0.00 |
The model with two separate splines and 4 df is again the best model in the set. We obtain the estimate of abundance and look at the estimated relationship between the length and the probability of capture (Figure 14)
nop.est.length.sp2.df4 <- Petersen::LP_est(nop.fit.length.sp2.df4, N_hat=~1)
est.p <- nop.est.length.sp2.df4$detail$data.expand
ggplot(data=est.p, aes(x=length, y=p, color=as.factor(..time)))+
geom_point()+
geom_line(size=.1)+
scale_color_discrete(name="Sample\nevent")+
xlab("Length (in)")+
ylab("Estimated p(capture)")We see that the relationship at time 1 is quite peaked but not so much for sampling event 2 which is in accordance to the results from classifying length into discrete bins. This spline model seems to indicate a very high catchability of very large fish at the first sampling event, something that was missed when the simple quadratic curve was used.
This model also shows a positive association between catchability at the two sampling events (Figure 15)
est.p <- nop.est.length.sp2.df4$detail$data.expand
temp <- tidyr::pivot_wider(est.p,
id_cols=c("..index", "length"),
values_from="p",
names_from="..time",
names_prefix="t")
ggplot(data=temp, aes(x=t1, y=t2, color=length))+
geom_point()+
scale_color_continuous(name="Length")+
xlab("Estimated p(capture) at sample event 1")+
ylab("Estimated p(capture) at sample event 2")The odd shape to the relationship is an artefact of two spline curves and the differing relationship between the ascending/descending arms of the spline. The above fit implies a positive correlation between the two capture probabilities which implies that the pooled-Petersen estimator will have a negative bias as seen in the model averaged results (Table 22).
nop.est.length.sp2.df4$summary
## N_hat_f N_hat_rn N_hat N_hat_SE N_hat_conf_level N_hat_conf_method
## 1 ~1 (Intercept) 60485.41 12635.26 0.95 logN
## N_hat_LCL N_hat_UCL p_model
## 1 40163.97 91088.72 ~..time + bs(ls, df = 4) + ..time:bs(ls, df = 4)
## name_model cond.ll n.parms nobs
## 1 p: ~..time + bs(ls, df = 4) + ..time:bs(ls, df = 4) -3565.507 10 7805
## method
## 1 CondLikFinally, we can again do the model averaging (Table 22):
# extract the estimates of the abundance
nop.length.class.ma.N_hat_length.class<- LP_modavg(
nop.fit.time,
nop.fit.length.class.time,
nop.fit.length.class.p.time,
nop.fit.eq.t1,
nop.fit.eq.t2,
nop.fit.length.quad1,
nop.fit.length.quad2,
nop.fit.length.sp2.df4, nop.fit.length.sp2.df5, N_hat=~1) Modnames | AICcWt | Estimate | SE |
|---|---|---|---|
p: ~..time + bs(ls, df = 4) + ..time:bs(ls, df = 4) | 0.85 | 60,485 | 12,635 |
p: ~..time + bs(ls, df = 5) + ..time:bs(ls, df = 5) | 0.14 | 59,567 | 10,895 |
p: ~..time + ls + I(ls^2) + ..time:ls + ..time:I(ls^2) | 0.00 | 59,210 | 9,366 |
p: ~-1 + I(as.numeric(..time == 1)) + I(as.numeric(..time == 2)):length.class | 0.00 | 49,536 | 3,629 |
p: ~-1 + length.class:..time | 0.00 | 60,614 | 13,039 |
p: ~-1 + I(as.numeric(..time == 2)) + I(as.numeric(..time == 1)):length.class | 0.00 | 49,536 | 3,629 |
p: ~length.class + ..time | 0.00 | 93,218 | 39,716 |
p: ~-1 + ..time | 0.00 | 49,536 | 3,629 |
p: ~..time + ls + I(ls * 2) | 0.00 | 49,563 | 3,635 |
Model averaged | 60,351 | 12,398 |
The spline model is so much a better fit that it overwhelms the other models and the model averaged estimate is basically the first model. Notice that the model averaged confidence interval is larger than the original model because the variation in estimates among the models has also been taken into account.
The use of a spline fit is an alternative to the methods of Chen and LLoyd (2000) who used a non-parametric smoother to estimate the catchabilities at each sampling event. The advantage of the spline method is that the AICc framework can be used to rank the various models.
7.3 Non-parametric smoothing
Chen and Lloyd (2000) developed a non-parametric smoother for the relationship between a continuous covariate and the catchability at the sample events. The data are divided into bins, a stratified-Petersen estimator is used on each bin, and a smoother is used to avoid the capture probabilities or the abundance estimates from varying wildly between successive bins.
The default fit is obtained using:
# fit the Chen and Lloyd estimator using default bin width
data(data_NorthernPike)
nop.CL <- Petersen::LP_CL_fit(data_NorthernPike, covariate="length")A plot of the recapture probabilities shows the upwards recapture probabilities with the larger lengths (Figure 16)
nop.CL$fit$plot1And a plot of the abundance as a function of length along with the estimated overall abundance (Figure 17)
nop.CL$fit$plot2
nop.CL$summary
## N_hat_f N_hat_rn N_hat N_hat_SE N_hat_conf_level N_hat_conf_method
## 1 ~1 (Intercept) 56620.94 5509.565 0.95 logN
## N_hat_LCL N_hat_UCL p_model cond.ll n.parms nobs method
## 1 46789.66 68517.92 NA NA NA 7805 ChenLloydThe estimated abundance is comparable to the estimates from the using the semi-parametric spline method with a smaller standard error.
Because this is a non-parametric fit, it is not possible to compute a likelihood value and so AICc methods can not be used to compare this model with the previous models. However, the spline fit has a comparable flexibility and fits nicely into the AICc framework.
More bins leads to a “wigglier fit” and some playing with the smoothing parameters is needed to avoid spikes in abundance which are artefacts of the small sample sizes (especially recaptures) in the smaller bins seen around lengths of 40 inches or higher. Generally speaking, the smaller the bins, the larger the smoothing standard deviation and vice-verso.
# fit the Chen and Lloyd estimator with lower smoothing parameter
data(data_NorthernPike)
old.centers <- nop.CL$covar.data$center
nop.CL2 <- Petersen::LP_CL_fit(data_NorthernPike, covariate="length",
centers=seq(17, 43,1), h1=1.5, h2=1.5)
nop.CL2$fit$plot1nop.CL2$fit$plot2nop.CL2$summary
## N_hat_f N_hat_rn N_hat N_hat_SE N_hat_conf_level N_hat_conf_method
## 1 ~1 (Intercept) 56982.7 5642.788 0.95 logN
## N_hat_LCL N_hat_UCL p_model cond.ll n.parms nobs method
## 1 46930.12 69188.58 NA NA NA 7805 ChenLloyd8 Accounting for heterogeneity III - geographic or temporal stratification
8.1 Introduction
In some cases, heterogeneity in catchability at both sampling events is related to the location where the fish was sampled (i.e., geographical stratification) or the date when the fish was sampled (temporal stratification) or both.
Data consists of the number of fish releases in each of \(s\) release strata (\(n_{1s}\)), which are recaptured in one of \(t\) recapture strata, leading to an \(s \times t\) recapture matrix (\(m_{ij}\)). Finally, there are \(n_{2t}\) unmarked fish captured for the first time in the second sampling event in the \(t\) recapture strata.
The key difference between these two cases is that in geographic stratification, it is theoretically possible to move from any one geographic stratum to any other geographic stratum leading to a general movement matrix. However, in temporal stratification, you cannot capture the fish at the second sampling event before it is released, leading to recapture matrices that have zeros on the lower diagonal.
Schaefer (1951) developed an estimate of the total population abundance, \(N\), using ratio and expectation arguments. The Schaefer estimate is biased unless capture probabilities are equal in all initial strata or the recovery probabilities are the same in all the final strata. If either condition holds, the pooled Petersen will also be unbiased and will be more precise (it makes more efficient use of the data). No estimate of standard error (s.e.) is available for the Schaefer estimate. Consequently, the use of the Schaefer (1951) estimator is no longer recommended
Seber (1982) summarizes the early work of Chapman and Junge (1956) and Darroch (1961). There are 3 cases:(a) \(s=t\); (b) \(s<t\); and (c) \(s>t\). In case (a), the recapture matrix (\(m\)) is square, and a simple matrix-based estimator is available. Both the initial and final stratum (population) abundances can be estimated. This estimate is commonly referred to as the Darroch estimate. They gave the necessary and sufficient conditions for the pooled Petersen to be unbiased and developed two chi-square tests for sufficient conditions (i.e., if the tests fail to detect an effect, it may “safe” to pool…if tests detect an effect, it may or may not be safe to pool).These are the two \(\chi^2\) tests presented earlier.
In case (b), only the initial stratum (population) abundances can be estimated, and in case (c) only the final stratum abundances can be estimated. The total population size, \(N\), is nevertheless estimable. Plante (1990) developed an alternate maximum likelihood method for the Darroch estimate that can be applied to all 3 cases including the cases where \(s \ne t\).
A key issue with geographic stratification, is that it is very sensitive to singularities in the recapture matrix. For example, it fails if any row is a multiple of other rows, or a linear combination of other rows. It leads to estimates with very large standard errors (and nonsensical stratum estimates) if the recapture matrix is close to singularity.
This often requires pooling of rows or columns to reduce the singularity of the recapture matrix. Schwarz and Taylor (1998) review the estimators for geographic stratification and provides guidance on how to pool rows or columns. This data are also often sparse requiring much pooling. This is difficult to do in a structured fashion. If all rows are pooled to a single row, or all columns pooled to a single column, the estimator reduces to a Pooled-Petersen estimator.
Arnason et al (1996) created a Windows program (SPAS) to help in the analysis of geographical stratification. Schwarz (2023) ported the functionality to R and included “logical pooling” so that different poolings could be compared using AIC etc. The Petersen package provides a wrapper to make it easier to use. The SPAS software also includes an autopool() function.
While SPAS could also be used for temporal stratification, but the problem is that there is no way to use the “structural zeros” representing fish being captured before being released, or fish being recaptured more than a small number of weeks after being released. This gives a diagonal or band-diagonal structure to the temporally stratified data which SPAS ignores.
Bjorkstedt (2000). created the DARR (Darroch Analysis with Rank-Reduction) computer program to automatically pool the above sparse matrices but this program uses simple rules to ensure that adequate sample sizes are available in each of the release and recovery strata. It ignores the highly structured form of the data and cannot deal with many problems commonly encountered in such data such as missing strata. In response to this, Bonner and Schwarz (2011) developed BTSPAS which uses a Bayesian approach with a hierarchical model for the capture probabilities to share information when data are spares, and a spline for the run shape to again share information and to provide a straightforward way to interpolate over missing data. Again, a wrapper is provided in the Petersen package to simplify usage of BTSPAS.
8.2 Geographic stratification
8.2.1 Sampling protocol
Consider an study to estimate the number of return salmon to a river. The returns extends over several weeks and there are several spawning sites. As the adult salmon return, they are captured and marked with individually numbered tags and released at the first capture location using, for example, a fishwheel. The migration continues, and stream walks of the spawning grounds notes the number of tagged and untagged fish..
The efficiency of the fishwheels varies over time in response to stream flow, run size passing the wheel and other uncontrollable events. So it is unlikely that the capture probabilities are equal over time, i.e. are heterogeneous over time. Similarly, the effort at the spawning grounds varies by ground and is also heterogeneous.
This is a form of temporal x geographical stratification – the key feature in geographical stratification is that fish from any of the tagging strata, can, in theory, go to any of the recovery strata. There is no “natural” ordering of the geographical strata; the temporal strata have a natural ordering.
In the more general case, both strata are “geographically stratified”.
8.2.2 Data structure
The same data structure as previously seen is also used, except the capture history is modified to account for potentially many geographical or temporal strata as follows:
- xx..yy represents a capture_history where xx and yy are the temporal or geographical stratum (e.g., julian week or spawning area) and ‘..’ separates the two strata from the two sampling event. If a fish is released in a stratum xx and never captured again, then yy is set to 0; if a fish is newly captured in stratum yy, then xx is set to zero.
- frequency variable for the number of fish with this capture history
- other covariates for the stratum yy.
It is not possible to model the initial capture probability or to separate fish by additional stratification variables in the SPAS software. These have rarely found to be useful in the geographically stratified models.
Some care is needed to properly account for 0 or missing values. Strata with 0 releases, should be dropped from the data structure. Similarly, strata with 0 recapture and 0 newly tagged fish should also be dropped. As shown later, some pooling of sparse rows/columns may be needed.
8.2.3 Key assumptions
The new key assumptions for this method are:
- all marked fish move to the recovery strata in the same proportions as unmarked fish in any release stratum
- there is no fall back of tagged fish, i.e., after marking the marked fish continue on their migration in same fashion as unmarked fish.
- catchability of marked fish represents the catchability of the unmarked fish
Unfortunately, for most of these assumptions, there is little information in the data that help detect violations. Gross violations of this model can be detected from the goodness-of-fit tests presented in Arnason et al. (1996) and the output from SPAS when the number of rows is not equal to the number of columns.
8.2.4 Harrison River Example
Returning salmon were captured and tags at a down river trap. A colored tag that varied by week of capture was applied. During the spawning season, stream walks took place at several spawning sites where the number of tags by color and the number of untagged fish was recorded on a weekly basis.
This is a combination of temporal stratification (when tags applied) and geographic stratification the spawning areas.
Here is part of the data:
data(data_spas_harrison)
head(data_spas_harrison, n=10) cap_hist freq
1 01..00 130
2 02..00 330
3 03..00 790
4 04..00 667
5 05..00 309
6 06..00 65
7 00..a 744
8 01..a 4
9 02..a 12
10 03..a 7
Because we allow the stratum labels to be longer than a single digit, we use the “..” to separate strata labels in the capture history.
In week 1, 130 fish were tagged and never seen again; 4 fish were tagged in week 1 and recovered in area a, etc. This data can be summarized into a matrix:
fw2
fw1 00 a b c d e f
00 0 744 1187 2136 951 608 127
01 130 4 2 1 1 0 0
02 330 12 7 14 1 3 0
03 790 7 11 41 9 1 1
04 667 1 13 40 12 9 1
05 309 0 1 8 8 3 0
06 65 0 0 0 0 0 1
The first row (corresponding to fw1=0) are the number of unmarked fish recovered in spawning area a. The first column (corresponding to fw2=0) are the number of released marked fish that were never seen again. The matrix in the lower bottom of the above array shows the number of fish released in each temporal stratum and recaptured in each spawning area.
8.2.5 Fitting the SPAS model
The SPAS model is fit to the above data using the wrapper supplied with this package. If a finer control is wanted on the fit, please refer to the documentation from the SPAS package. The very sparse last row will make fitting the model to the original data difficult with a very flat likelihood surface and so we relax the convergence criteria:
The row.pool.in and col.pool.in inform the function on which rows or columns to pool before the analysis proceeds. Both parameters use a vector of codes (length \(s\) for row pooing and length \(t\) for column pooling) where rows/columns are pooled that share the same value.
For example. row.pool.in=c(1,2,3,4,5,6) would imply that no rows are pooled, while row.pool.in=c('a','a','a','b','b','b') would imply that the first three rows and last three rows are pooled. The entries in the vector can be numeric or character; however, using character entries implies that the final pooled matrix is displayed in the order of the character entries. I find that using entries such as '123' to represent pooling rows 1, 2, and 3 to be easiest to use.
The SPAS system only fits models were the number of rows after pooling is less than or equal to the number of columns after pooling.
8.2.6 Results from model 1 (no pooling).
The summary of the fit is:
mod..1$summary p_model name_model cond.ll n.parms nobs method
1 Refer to row.pool/col.pool No restrictions 47243.45 48 8256 SPAS
cond.factor
1 4121.288
The usual conditional likelihood is presented etc. Of more importance is the condition factor. This indicated how close to singularity the recovery matrix is with larger values indicating closer to singularity. Usually, this value should be 1000 or less to avoid numerical issues in the fit.
The results of the model fit is a LARGE list. But the SPAS.print.model() function produces a nice report
SPAS::SPAS.print.model(mod..1$fit)Model Name: No restrictions
Date of Fit: 2025-10-24 15:54
Version of OPEN SPAS used : SPAS-R 2025.2.1
Raw data
a b c d e f
01 4 2 1 1 0 0 130
02 12 7 14 1 3 0 330
03 7 11 41 9 1 1 790
04 1 13 40 12 9 1 667
05 0 1 8 8 3 0 309
06 0 0 0 0 0 1 65
744 1187 2136 951 608 127 0
Row pooling setup : 1 2 3 4 5 6
Col pooling setup : 1 2 3 4 5 6
Physical pooling : FALSE
Theta pooling : FALSE
CJS pooling : FALSE
Chapman estimator of population size 70135 (SE 4503 )
Raw data AFTER PHYSICAL (but not logical) POOLING
pool1 pool2 pool3 pool4 pool5 pool6
pool.1 4 2 1 1 0 0 130
pool.2 12 7 14 1 3 0 330
pool.3 7 11 41 9 1 1 790
pool.4 1 13 40 12 9 1 667
pool.5 0 1 8 8 3 0 309
pool.6 0 0 0 0 0 1 65
744 1187 2136 951 608 127 0
Condition number of XX' where X= (physically) pooled matrix is 4121.288
Condition number of XX' after logical pooling 4121.288
Large value of kappa (>1000) indicate that rows are approximately proportional which is not good
Conditional Log-Likelihood: 47243.45 ; np: 48 ; AICc: -94390.9
Code/Message from optimization is: 0 relative convergence (4)
Estimates
pool1 pool2 pool3 pool4 pool5 pool6 psi cap.prob exp factor
pool.1 3.7 2.6 0.8 0.9 0.0 0 130 0.005 191.2
pool.2 12.0 7.0 14.0 1.0 3.0 0 330 1.000 0.0
pool.3 7.0 11.0 41.0 9.0 1.0 1 790 1.000 0.0
pool.4 1.0 13.8 37.5 11.8 10.9 1 667 0.021 47.6
pool.5 0.0 1.0 7.7 7.9 3.3 0 309 0.037 26.3
pool.6 0.0 0.0 0.0 0.0 0.0 1 65 0.012 79.4
est unmarked 744.0 1186.0 2139.0 951.0 606.0 127 0 NA NA
Pop Est
pool.1 26523
pool.2 367
pool.3 860
pool.4 36104
pool.5 8998
pool.6 5307
est unmarked 78159
SE of above estimates
pool1 pool2 pool3 pool4 pool5 pool6 psi cap.prob exp factor
pool.1 1.6 1.3 0.8 1.0 0.0 0 11.4 0.002 83.1
pool.2 3.5 2.6 3.7 1.0 1.7 0 18.2 0.000 0.0
pool.3 2.6 3.3 6.4 3.0 1.0 1 28.1 0.000 0.0
pool.4 1.0 3.6 5.9 3.5 2.1 1 25.8 0.007 16.7
pool.5 0.0 1.0 2.7 2.9 2.0 0 17.6 0.072 53.7
pool.6 0.0 0.0 0.0 0.0 0.0 1 8.1 0.015 94.7
est unmarked NA NA NA NA NA NA 0.0 NA NA
Pop Est
pool.1 11462
pool.2 0
pool.3 0
pool.4 12411
pool.5 17661
pool.6 6253
est unmarked 14676
Chisquare gof cutoff : 0.1
Chisquare gof value : 0.843434
Chisquare gof df : 0
Chisquare gof p : NA
The original data, the data after pooling, estimates and their standard errors are shown. Here the stratified-Petersen estimate of the total number of fish passing the first sampling station is 78,159 with a standard error of 14,676.
The N entries refer to the population size; the N.stratum entries refer to the individual stratum population sizes; the cap entries refer to the estimated probability of capture in each row stratum; the exp.factor entries refer to (1-cap)/cap, or the expansion factor for each row; the psi entries refer to the number of animals tagged but never seen again (the right most column in the input data); and the theta entries refer to the expected number of animals that were tagged in row stratum \(i\) and recovered in column stratum \(j\) (after pooling).
The fit is not entirely satisfactory because notice the very small population estimates for in weeks 2 and 3 or releases. This is unrealistic and is an indication of potential singularity problems in the data as noted with the large condition number seen earlier.
You can extract parts of the “printed” output by using the extract=TRUE argument in the SPAS.print.model() function:
# demonstrate how to extract part of output
mod..1.res <- SPAS::SPAS.print.model(mod..1$fit, extract=TRUE)
names(mod..1.res)[1] "model_name" "date" "version" "input" "Chapman"
[6] "fit" "spas" "gof"
mod..1.res$spas$estimate pool1 pool2 pool3 pool4 pool5 pool6 psi cap.prob exp factor
pool.1 3.7 2.6 0.8 0.9 0.0 0 130 0.005 191.2
pool.2 12.0 7.0 14.0 1.0 3.0 0 330 1.000 0.0
pool.3 7.0 11.0 41.0 9.0 1.0 1 790 1.000 0.0
pool.4 1.0 13.8 37.5 11.8 10.9 1 667 0.021 47.6
pool.5 0.0 1.0 7.7 7.9 3.3 0 309 0.037 26.3
pool.6 0.0 0.0 0.0 0.0 0.0 1 65 0.012 79.4
est unmarked 744.0 1186.0 2139.0 951.0 606.0 127 0 NA NA
Pop Est
pool.1 26523
pool.2 367
pool.3 860
pool.4 36104
pool.5 8998
pool.6 5307
est unmarked 78159
mod..1.res$spas$se pool1 pool2 pool3 pool4 pool5 pool6 psi cap.prob exp factor
pool.1 1.6 1.3 0.8 1.0 0.0 0 11.4 0.002 83.1
pool.2 3.5 2.6 3.7 1.0 1.7 0 18.2 0.000 0.0
pool.3 2.6 3.3 6.4 3.0 1.0 1 28.1 0.000 0.0
pool.4 1.0 3.6 5.9 3.5 2.1 1 25.8 0.007 16.7
pool.5 0.0 1.0 2.7 2.9 2.0 0 17.6 0.072 53.7
pool.6 0.0 0.0 0.0 0.0 0.0 1 8.1 0.015 94.7
est unmarked NA NA NA NA NA NA 0.0 NA NA
Pop Est
pool.1 11462
pool.2 0
pool.3 0
pool.4 12411
pool.5 17661
pool.6 6253
est unmarked 14676
cat("\n\nEstimated total abundance ", mod..1.res$spas$estimate[nrow(mod..1.res$spas$estimate), ncol(mod..1.res$spas$estimate)],
"(SE ", mod..1.res$spas$se[nrow(mod..1.res$spas$estimate), ncol(mod..1.res$spas$estimate)], ") fish", "\n")
Estimated total abundance 78159 (SE 14676 ) fish
8.2.7 Pooling some rows and columns
As noted by Darroch (1961), the stratified-Petersen will fail if the matrix of movements is close to singular. This often happens if two rows are proportional to each other. In this case, there is no unique MLE for the probability of capture in the two rows, and they should be pooled. A detailed discussion of pooling is found in Schwarz and Taylor (1998).
There is no simple way to determine which rows/column to pool but when estimated population sizes are small for a stratum, this is usual an indication that some pooling is required. The SPAS system has an experimental autopool feature which may serve as a guide.
8.2.7.1 Pooling pairs of rows
Let us now pool the first two rows, the next two rows, and the last two rows,
The code is
mod..2 <- Petersen::LP_SPAS_fit(data_spas_harrison, model.id="Pooling every second row",
row.pool.in=c("12","12","34","44","56","56"),
col.pool.in=c(1,2,3,4,5,6))Using nlminb to find conditional MLE
outer mgc: 1967.318
outer mgc: 1585.784
outer mgc: 601.797
outer mgc: 361.6262
outer mgc: 255.3465
outer mgc: 301.4938
outer mgc: 25.14831
outer mgc: 2.82591
outer mgc: 2.424709
outer mgc: 16.30222
outer mgc: 4.565925
outer mgc: 24.77543
outer mgc: 57.44612
outer mgc: 7.92634
outer mgc: 11.63666
outer mgc: 10.76265
outer mgc: 3.863489
outer mgc: 13.76323
outer mgc: 26.44275
outer mgc: 4.706843
outer mgc: 23.51753
outer mgc: 0.8778394
outer mgc: 5.614518
outer mgc: 1.738815
outer mgc: 5.426214
outer mgc: 16.44758
outer mgc: 1.748598
outer mgc: 1.453996
outer mgc: 6.546109
outer mgc: 6.563646
outer mgc: 8.584827
outer mgc: 20.45095
outer mgc: 2.996709
outer mgc: 1.732739
outer mgc: 5.660383
outer mgc: 6.150282
outer mgc: 6.135996
outer mgc: 10.84269
outer mgc: 2.233833
outer mgc: 5.003054
outer mgc: 2.24289
outer mgc: 2.801219
outer mgc: 0.6797359
outer mgc: 0.7992463
outer mgc: 0.06792093
outer mgc: 0.1106809
outer mgc: 0.04946835
outer mgc: 0.02579226
outer mgc: 0.01303348
outer mgc: 0.006503766
outer mgc: 0.003219488
outer mgc: 0.001356174
outer mgc: 0.001004277
outer mgc: 0.0005343734
outer mgc: 0.00013112
Convergence codes from nlminb 1 singular convergence (7)
Finding conditional estimate of N
#mod..2$summaryNotice how we specify the pooling for rows and columns and the choice of entries for the two corresponding vectors. Now the condition factor is much better (well less than 1000).
The results of the model fit is
Model Name: Pooling every second row
Date of Fit: 2025-10-24 15:54
Version of OPEN SPAS used : SPAS-R 2025.2.1
Raw data
a b c d e f
01 4 2 1 1 0 0 130
02 12 7 14 1 3 0 330
03 7 11 41 9 1 1 790
04 1 13 40 12 9 1 667
05 0 1 8 8 3 0 309
06 0 0 0 0 0 1 65
744 1187 2136 951 608 127 0
Row pooling setup : 12 12 34 44 56 56
Col pooling setup : 1 2 3 4 5 6
Physical pooling : FALSE
Theta pooling : FALSE
CJS pooling : FALSE
Chapman estimator of population size 70135 (SE 4503 )
Raw data AFTER PHYSICAL (but not logical) POOLING
pool1 pool2 pool3 pool4 pool5 pool6
pool.12 4 2 1 1 0 0 130
pool.12 12 7 14 1 3 0 330
pool.34 7 11 41 9 1 1 790
pool.44 1 13 40 12 9 1 667
pool.56 0 1 8 8 3 0 309
pool.56 0 0 0 0 0 1 65
744 1187 2136 951 608 127 0
Condition number of XX' where X= (physically) pooled matrix is 4121.288
Condition number of XX' after logical pooling 189.4612
Large value of kappa (>1000) indicate that rows are approximately proportional which is not good
Conditional Log-Likelihood: 47242.37 ; np: 46 ; AICc: -94392.74
Code/Message from optimization is: 1 singular convergence (7)
Estimates
pool1 pool2 pool3 pool4 pool5 pool6 psi cap.prob exp factor
pool.12 3.5 2.8 0.9 1 0.0 0.0 130 0.019 52.1
pool.12 10.4 10.0 12.4 1 3.1 0.0 330 0.019 52.1
pool.34 7.0 11.0 41.0 9 1.0 1.0 790 1.000 0.0
pool.44 0.9 15.3 37.5 12 9.1 1.1 667 0.036 26.6
pool.56 0.0 1.6 6.9 8 3.1 0.0 309 0.015 66.2
pool.56 0.0 0.0 0.0 0 0.0 1.5 65 0.015 66.2
est unmarked 746.0 1180.0 2141.0 951 608.0 126.0 0 NA NA
Pop Est
pool.12 7327
pool.12 19484
pool.34 860
pool.44 20470
pool.56 22123
pool.56 4438
est unmarked 74701
SE of above estimates
pool1 pool2 pool3 pool4 pool5 pool6 psi cap.prob exp factor
pool.12 1.8 1.9 0.9 1.0 0.0 0.0 11.4 0.006 15.6
pool.12 3.3 3.0 3.2 1.0 1.5 0.0 18.2 0.006 15.6
pool.34 2.6 3.3 6.4 3.0 1.0 1.0 28.1 0.000 0.0
pool.44 0.9 4.4 6.6 3.4 2.7 1.1 25.8 0.021 16.0
pool.56 0.0 1.7 2.3 2.6 1.4 0.0 17.6 0.009 39.5
pool.56 0.0 0.0 0.0 0.0 0.0 0.7 8.1 0.009 39.5
est unmarked NA NA NA NA NA NA 0.0 NA NA
Pop Est
pool.12 2149
pool.12 5715
pool.34 0
pool.44 11887
pool.56 13007
pool.56 2609
est unmarked 10284
Chisquare gof cutoff : 0.1
Chisquare gof value : 2.857233
Chisquare gof df : 2
Chisquare gof p : 0.2396402
Here the stratified-Petersen estimate of the total number of smolts passing the first sampling station is 74,701 with a standard error of 74,701. which is a slight reduction from the unpooled estimates.
The estimates look better, but a standard error of 0 for the abundance in some strata is an indication that the fit is not very realistic.
8.2.7.2 Pooling to early vs late.
Let us now pool the first three rows and the last three rows,
The code is
mod..3 <- Petersen::LP_SPAS_fit(data_spas_harrison, model.id="Pooling early vs. late",
row.pool.in=c("123","123","123","456","456","456"),
col.pool.in=c(1,2,3,4,5,6))Using nlminb to find conditional MLE
outer mgc: 2986.733
outer mgc: 1769.526
outer mgc: 816.8674
outer mgc: 269.1311
outer mgc: 30.10549
outer mgc: 24.07398
outer mgc: 5.393645
outer mgc: 18.96964
outer mgc: 2.953744
outer mgc: 1.395084
outer mgc: 18.87373
outer mgc: 6.688677
outer mgc: 1.640811
outer mgc: 7.332616
outer mgc: 1.685392
outer mgc: 7.317009
outer mgc: 1.522422
outer mgc: 6.294555
outer mgc: 1.261084
outer mgc: 4.980596
outer mgc: 2.103006
outer mgc: 8.561154
outer mgc: 1.79518
outer mgc: 6.70074
outer mgc: 2.203129
outer mgc: 8.175411
outer mgc: 2.210091
outer mgc: 7.714625
outer mgc: 3.180497
outer mgc: 11.01373
outer mgc: 4.797201
outer mgc: 18.68681
outer mgc: 10.12453
outer mgc: 12.11322
outer mgc: 6.303981
outer mgc: 6.197803
outer mgc: 2.248121
outer mgc: 0.7088488
outer mgc: 0.5721706
outer mgc: 0.1888875
outer mgc: 0.07641965
outer mgc: 0.02903072
outer mgc: 0.01084322
outer mgc: 0.004013247
outer mgc: 0.001470131
outer mgc: 0.0001335366
outer mgc: 9.781857e-06
Convergence codes from nlminb 1 singular convergence (7)
Finding conditional estimate of N
#mod..3$summaryNotice how we specify the pooling for rows and columns and the choice of entries for the two corresponding vectors. Now the condition factor is again much better (well less than 1000).
The results of the model fit is
Model Name: Pooling early vs. late
Date of Fit: 2025-10-24 15:54
Version of OPEN SPAS used : SPAS-R 2025.2.1
Raw data
a b c d e f
01 4 2 1 1 0 0 130
02 12 7 14 1 3 0 330
03 7 11 41 9 1 1 790
04 1 13 40 12 9 1 667
05 0 1 8 8 3 0 309
06 0 0 0 0 0 1 65
744 1187 2136 951 608 127 0
Row pooling setup : 123 123 123 456 456 456
Col pooling setup : 1 2 3 4 5 6
Physical pooling : FALSE
Theta pooling : FALSE
CJS pooling : FALSE
Chapman estimator of population size 70135 (SE 4503 )
Raw data AFTER PHYSICAL (but not logical) POOLING
pool1 pool2 pool3 pool4 pool5 pool6
pool.123 4 2 1 1 0 0 130
pool.123 12 7 14 1 3 0 330
pool.123 7 11 41 9 1 1 790
pool.456 1 13 40 12 9 1 667
pool.456 0 1 8 8 3 0 309
pool.456 0 0 0 0 0 1 65
744 1187 2136 951 608 127 0
Condition number of XX' where X= (physically) pooled matrix is 4121.288
Condition number of XX' after logical pooling 22.90096
Large value of kappa (>1000) indicate that rows are approximately proportional which is not good
Conditional Log-Likelihood: 47237.51 ; np: 44 ; AICc: -94387.01
Code/Message from optimization is: 1 singular convergence (7)
Estimates
pool1 pool2 pool3 pool4 pool5 pool6 psi cap.prob exp factor
pool.123 4.8 2.5 0.8 1.1 0.0 0.0 130 0.038 25.4
pool.123 14.4 8.8 10.9 1.1 3.9 0.0 330 0.038 25.4
pool.123 8.4 13.9 31.9 9.8 1.3 1.4 790 0.038 25.4
pool.456 1.2 17.1 30.1 13.2 12.1 1.5 667 0.033 29.2
pool.456 0.0 1.3 6.0 8.8 4.0 0.0 309 0.033 29.2
pool.456 0.0 0.0 0.0 0.0 0.0 1.5 65 0.033 29.2
est unmarked 739.0 1177.0 2160.0 948.0 603.0 126.0 0 NA NA
Pop Est
pool.123 3642
pool.123 9685
pool.123 22695
pool.456 22445
pool.456 9939
pool.456 1994
est unmarked 70399
SE of above estimates
pool1 pool2 pool3 pool4 pool5 pool6 psi cap.prob exp factor
pool.123 2.3 1.7 0.8 1.1 0.0 0.0 11.4 0.007 4.8
pool.123 3.8 3.1 2.9 1.1 2.2 0.0 18.2 0.007 4.8
pool.123 3.0 3.7 4.7 3.0 1.3 1.3 28.1 0.007 4.8
pool.456 1.3 3.9 4.4 3.2 2.9 1.2 25.8 0.006 5.8
pool.456 0.0 1.3 2.1 2.8 2.1 0.0 17.6 0.006 5.8
pool.456 0.0 0.0 0.0 0.0 0.0 1.2 8.1 0.006 5.8
est unmarked NA NA NA NA NA NA 0.0 NA NA
Pop Est
pool.123 664
pool.123 1767
pool.123 4140
pool.456 4299
pool.456 1904
pool.456 382
est unmarked 4552
Chisquare gof cutoff : 0.1
Chisquare gof value : 12.99086
Chisquare gof df : 4
Chisquare gof p : 0.01132054
Here the stratified-Petersen estimate of the total number of smolts passing the first sampling station is 70,399 with a standard error of 70,399. which is a slight reduction from the unpooled estimates.
The estimates seem more sensible.
8.2.7.3 Pooling to a single row and complete pooling
You can pool to a single row (and multiple columns) or a single row and single column both of which are equivalent to the pooled Petersen estimator. The code and output follow:
Using nlminb to find conditional MLE
outer mgc: 5554.604
outer mgc: 3255.445
outer mgc: 686.8353
outer mgc: 85.66413
outer mgc: 12.0596
outer mgc: 3.803003
outer mgc: 0.6639956
outer mgc: 0.2609515
outer mgc: 0.09867538
outer mgc: 0.03679076
outer mgc: 0.01360926
outer mgc: 0.005017272
outer mgc: 0.001859472
outer mgc: 0.0002086563
outer mgc: 1.313641e-05
Convergence codes from nlminb 1 singular convergence (7)
Finding conditional estimate of N
Model Name: A single row
Date of Fit: 2025-10-24 15:54
Version of OPEN SPAS used : SPAS-R 2025.2.1
Raw data
a b c d e f
01 4 2 1 1 0 0 130
02 12 7 14 1 3 0 330
03 7 11 41 9 1 1 790
04 1 13 40 12 9 1 667
05 0 1 8 8 3 0 309
06 0 0 0 0 0 1 65
744 1187 2136 951 608 127 0
Row pooling setup : 1 1 1 1 1 1
Col pooling setup : 1 2 3 4 5 6
Physical pooling : FALSE
Theta pooling : FALSE
CJS pooling : FALSE
Chapman estimator of population size 70135 (SE 4503 )
Raw data AFTER PHYSICAL (but not logical) POOLING
pool1 pool2 pool3 pool4 pool5 pool6
pool.1 4 2 1 1 0 0 130
pool.1 12 7 14 1 3 0 330
pool.1 7 11 41 9 1 1 790
pool.1 1 13 40 12 9 1 667
pool.1 0 1 8 8 3 0 309
pool.1 0 0 0 0 0 1 65
744 1187 2136 951 608 127 0
Condition number of XX' where X= (physically) pooled matrix is 4121.288
Condition number of XX' after logical pooling 1
Large value of kappa (>1000) indicate that rows are approximately proportional which is not good
Conditional Log-Likelihood: 47237.43 ; np: 43 ; AICc: -94388.87
Code/Message from optimization is: 1 singular convergence (7)
Estimates
pool1 pool2 pool3 pool4 pool5 pool6 psi cap.prob exp factor
pool.1 4.5 2.6 0.8 1.1 0.0 0.0 130 0.036 27.1
pool.1 13.6 8.9 10.7 1.1 4.2 0.0 330 0.036 27.1
pool.1 8.0 14.0 31.4 10.1 1.4 1.5 790 0.036 27.1
pool.1 1.1 16.6 30.6 13.5 12.5 1.5 667 0.036 27.1
pool.1 0.0 1.3 6.1 9.0 4.2 0.0 309 0.036 27.1
pool.1 0.0 0.0 0.0 0.0 0.0 1.5 65 0.036 27.1
est unmarked 741.0 1178.0 2160.0 947.0 602.0 125.0 0 NA NA
Pop Est
pool.1 3883
pool.1 10326
pool.1 24198
pool.1 20906
pool.1 9257
pool.1 1857
est unmarked 70426
SE of above estimates
pool1 pool2 pool3 pool4 pool5 pool6 psi cap.prob exp factor
pool.1 2.1 1.8 0.8 1.1 0.0 0.0 11.4 0.002 1.9
pool.1 3.0 3.1 2.8 1.1 2.2 0.0 18.2 0.002 1.9
pool.1 2.6 3.6 4.4 2.9 1.3 1.3 28.1 0.002 1.9
pool.1 1.1 3.8 4.4 3.2 2.9 1.3 25.8 0.002 1.9
pool.1 0.0 1.3 2.1 2.8 2.2 0.0 17.6 0.002 1.9
pool.1 0.0 0.0 0.0 0.0 0.0 1.3 8.1 0.002 1.9
est unmarked NA NA NA NA NA NA 0.0 NA NA
Pop Est
pool.1 262
pool.1 696
pool.1 1632
pool.1 1410
pool.1 624
pool.1 125
est unmarked 4545
Chisquare gof cutoff : 0.1
Chisquare gof value : 13.09369
Chisquare gof df : 5
Chisquare gof p : 0.0225164
Now the estimated abundance of 70,426 with a standard error of 4,545. which is a slight reduction from the unpooled estimates.
8.2.7.4 Comparing the different poolings:
We can compare the fit using AICc in the usual way (Table 23)
spas.aictab <- Petersen::LP_AICc(mod..1, mod..2, mod..3, mod..4)Model specification | Conditional log-likelihood | # parms | # obs | AICc | Delta | AICcWt |
|---|---|---|---|---|---|---|
Pooling every second row | 47,242.37 | 46 | 8,256 | -94,392.22 | 0.00 | 0.63 |
No restrictions | 47,243.45 | 48 | 8,256 | -94,390.32 | 1.89 | 0.24 |
A single row | 47,237.43 | 43 | 8,256 | -94,388.41 | 3.81 | 0.09 |
Pooling early vs. late | 47,237.51 | 44 | 8,256 | -94,386.53 | 5.69 | 0.04 |
Notice that even with a high degree of logical pooling, SPAS still estimates a movement probability for the entire recapture matrix. All that logical pooling does is enforce equality of the initial capture probabilities. It is possible to do physical row pooling where the recapture matrix is also reduced, but then you cannot compare different physical poolings using AIC.
We see that there is a slight preference for pooling every two rows vs no pooling, but the condition factor of the model with no pooling makes it less than ideal.
We can also create a report of the estimates and model average them in the usual way (Table 24).
Error in LP_SPAS_est(x): LP_SPAS argument must be the results of a call to fitting SPAS objectl
Modnames | AICcWt | Estimate | SE |
|---|---|---|---|
Pooling every second row | 0.63 | 74,701 | 10,284 |
No restrictions | 0.24 | 78,159 | 14,676 |
A single row | 0.09 | 70,426 | 4,545 |
Pooling early vs. late | 0.04 | 70,399 | 4,552 |
Model averaged | 74,986 | 11,252 |
Different column pooling will give the same fit and so cannot be compared. Refer to the vignette in the SPAS package on why column poolings cannot be compared for more details.
8.2.7.5 What does autopool suggest?
We can also try the autopooling options where SPAS pools rows and columns to ensure that sufficient data is present, but, (at this moment) does not check the singularity condition.
The autopooling function only suggests pooling the last 2 rows because the sample sizes are very small, but the condition factor is still large and so I would not consider this model.
8.2.9 Summary
The greatest problem that you will likely encounter while using SPAS is the near singularity of the recovery matrix. This is often unavoidable because there is no simple way to simplify the structure of the model and so all \(s \times t\) possible movement patterns must be accounted for. If the stratification is temporal, this imposes much additional structure that can be used (see next section). Consequently, I suspect you will find that more more than 3 or 4 rows or columns is about the limit that can successfully fit with SPAS in practice.
8.3 Temporal stratification
Temporal stratification is commonly used when estimating the run abundance of incoming adult salmon or outgoing juvenile salmon. The key difference from geographical stratification is that is is not possible for fish to be captured before they are releases leading to a large number of structural 0’s in the counts. The incoming/out coming abundance generally changes ‘slowly’ over time, so that the abundance in temporal stratum \(i\) has information on temporal stratum \(i+1\). Problems with the data are common, e.g. no fish released in some of the temporal strata, or no operations in other temporal strata, e.g., due to safety concerns leading to structural zeros.
Bonner and Schwarz (2011) developed a Bayesian model for temporally stratified sampling and created an \(R\) package, BTSPAS that analyses these studies. In this package, we provide a wrapper function to make it easier to use the BTSPAS package and to present results in a unified fashion. However, if finer control is wanted over the fitting procedures, the BTSPAS package can be used directly. Details about this model are presented in Bonner and Schwarz (2011) and in the vignettes that ship with the package. A synopsis of the theory is presented in Appendix D.
8.3.1 Sampling Protocol
Consider a study to estimate the number of outgoing smolts on a small river. The run of smolts extends over several weeks. As smolts migrate, they are captured and marked with individually numbered tags and released at the first capture location using, for example, a fishwheel. The migration continues, and a second fishwheel takes a second sample several kilometers down stream. At the second fishwheel, the captures consist of a mixture of marked (from the first fishwheel) and unmarked fish.
The efficiency of the fishwheels varies over time in response to stream flow, run size passing the wheel and other uncontrollable events. So it is unlikely that the capture probabilities are equal over time at either location, i.e. are heterogeneous over time.
We suppose that we can temporally stratify the data into, for example, weeks, where the capture-probabilities are (mostly) homogeneous at each wheel in each week.
8.3.2 Data structure
The same data structure as previously seen is also used, except the capture history is modified to account for potentially many temporal strata as follows:
- xx..yy represents a capture_history where xx and yy are the temporal stratum (e.g., julian week) and ‘..’ separates the two temporal strata. If a fish is released in temporal stratum and never captured again, then yy is set to 0; if a fish is newly captured in temporal stratum yy, then xx is set to zero.
- frequency variable for the number of fish with this capture history
- other covariates for this temporal stratum yy.
It is not possible to model the initial capture probability or to separate fish by stratification variables. These have rarely found to be useful in the temporally stratified models.
Some care is needed to properly account for 0 or missing values. For temporal strata with 0 releases, the BTSPAS wrappers will automatically impute 0 for the number of releases and recaptures if no capture history records are present. However, no imputation is done for strata is missing \(u_2\) values because this could represent a case were the trap was not running, rather than the trap did not capture any unmarked fish. The summary statistics should be be carefully checked when using this wrappers.
8.3.3 Key assumptions
The new key assumptions for this method are:
- sampling at second station is for the entire period of the stratum It is untrue, the user may need may need to impute and deal with the additional uncertainty
- all marked fish move at same rate as unmarked fish
- there is no fall back of tagged fish, i.e., after marking the marked fish continue on their migration in same fashion as unmarked fish.
- catchability of marked fish represents the catchability of the unmarked fish
Unfortunately, for most of these assumptions, there is little information in the data that help detect violations. Gross violations of this model can be detected from the goodness-of-fit plots presented in Bonner and Schwarz (2011).
There are two common cases
- Fish are stratified into temporal strata, and fish released in temporal stratum \(i\), move together and are captured together in a single future temporal stratum. This is called the Diagonal Model.
- Fish are stratified into temporal strata, but fish released in temporal stratum \(i\) can be captured in a number of future temporal strata. This is the called the NonDiagonal Case
The BTSPAS package also has other functions for dealing with multiple age classes in the study, but these are not discussed in this document.
8.3.4 Diagonal Model
In the diagonal model, fish in.a marked-cohort tend to move together and so tend to be recaptured close in time as well. Suppose that fish captured and marked in each week tend to migrate together so that they are captured in a single subsequent stratum. For example, suppose that in each julian week \(j\), \(n_{1j}\) fish are marked and released above the rotary screw trap. Of these, \(m_{2j}\) are recaptured. All recaptures take place in the week of release, i.e. the matrix of releases and recoveries is diagonal. The \(n_{1j}\) and \(m_{2j}\) establish the capture efficiency of the second trap in julian week \(j\).
At the same time, \(u_{2j}\) unmarked fish are captured at the screw trap.
We label the releases as \(n_{1i}\) to indicate this is the “first” capture and release of a cohort of fish, and \(m_{2i}\) or \(u_{2i}\) to indicate that this is “second” event where tagged fish are recaptured, and unmarked fish are newly capture.
Here is an example of data collected under this protocol:
data(data_btspas_diag1)
head(data_btspas_diag1) cap_hist freq logflow
1 00..04 14587 6.564691
2 04..00 1414 6.564691
3 04..04 51 6.564691
4 00..05 2854 7.077220
5 05..00 1189 7.077220
6 05..05 146 7.077220
In temporal stratum 4, 1465 fish were released at the first fishwheel, of which 51 were recaptured in the same week at the second fishwheel, and 1414 were never seen again. An additional 14587 unmarked fish were captured at the second fishwheel.
This can be summarized in a matrix format (up to week 10):
fw2
fw1 0 4 5 6 7 8 9 10 11 12
0 0 14587 2854 1027 1945 2855 1323 933 57549 14846
4 1414 51 0 0 0 0 0 0 0 0
5 1189 0 146 0 0 0 0 0 0 0
6 180 0 0 17 0 0 0 0 0 0
7 1167 0 0 0 168 0 0 0 0 0
8 1581 0 0 0 0 72 0 0 0 0
9 880 0 0 0 0 0 43 0 0 0
10 582 0 0 0 0 0 0 28 0 0
11 7672 0 0 0 0 0 0 0 297 0
12 5695 0 0 0 0 0 0 0 0 313
The first row (corresponding to fw1=0) are the number of unmarked fish recovered at the second fish wheel in the temporal strata. The first column (corresponding to fw2=0) are the number of released marked fish that were never seen again.
We can also get the summary statistics (\(n_1\), \(m_2\), and \(u_2\)) for this data:
# compute n, m,u
nmu <- Petersen::cap_hist_to_n_m_u(data_btspas_diag1)
temp <- data.frame(time=nmu$..ts, n1=nmu$n1, m2=nmu$m2, u2=nmu$u2)
temp time n1 m2 u2
1 4 1465 51 14587
2 5 1335 146 2854
3 6 197 17 1027
4 7 1335 168 1945
5 8 1653 72 2855
6 9 923 43 1323
7 10 610 28 933
8 11 7969 297 57549
9 12 6008 313 14846
10 13 3770 151 5291
11 14 4854 309 9249
12 15 3350 376 4615
13 16 1062 110 1433
14 17 346 40 446
15 18 88 12 120
16 19 20 1 23
There are no missing values
The theory in Appendix D, assumes that a single spline curve can be fit across all strata, but problems can arise in fitting this model to the data. In some cases, there are obvious breaks in the pattern of abundance over time that need to be accounted for in the model. F Attempting to fit a smooth curve across all strata ignores these jumps and so it is necessary to allow for breaks in the fitted spline.
It may occur that no marked fish (i.e., \(n_{1i}\) =0 for some \(i\)) are released in a particular stratum because no fish were available or because of logistical constraints. This would imply that a simple Petersen estimator for this stratum cannot be computed because no estimate of the capture probability is available. However, the Bayesian method will impute a range of capture-probabilities based on the capture probabilities in other strata, the shape of the spline curve, and the observed number of unmarked fish captured. The final estimate of abundance will (automatically) incorporate the uncertainty for this imputed capture probability.
If no data could be collected for a particular stratum (i.e., all of \(n_{1i}=0\), \(m_{2i}=0\), and \(u_{2i}=0\)), the spline will “impute” a value for the run size and capture probability in that stratum given the shape of the spline and the variability in individual run sizes about the spline; and will “impute” a value for the capture probability given the range of capture probabilities in the other strata. The final estimate of abundance will (automatically) incorporate the uncertainty for this imputed values.
While it is possible to interpolate for several strata in a row, there is of course, no information on the shape of the underlying spline during these missed strata, and so the results should be interpreted with care.
The Bayesian model assumes that sampling occurs throughout the temporal stratum. However, in some strata, sampling may take place in part of the stratum (i.e., in 3 of 7 days in a week). This causes no theoretical problem for estimation of the capture probability as the capture probability is assumed to be equal over the entire week so estimates of the probability of capture at the second trap based on 3 days may have poor precision but remain unbiased. However, the number of unmarked fish needs to be adjusted for the partial sampling during the stratum. We assume that the user has made this adjustment, and no accounting of the uncertainty in this adjustment will be made.
In some cases, the recapture effort varies over the course of a temporal stratum. For example, two rotary screw traps may be operating on Monday, and then only one trap is operating on Tuesday, etc. Unfortunately, this type of problem CANNOT be adequately dealt with by the spline (or any other method) that uses batch marks. The problem is that differing effort during a stratum (week) results in heterogeneity of catchability during the week, e.g., the catchability on days when two traps are operating is likely larger than the catchability on days when only one trap is operating. If a batch mark is used, the data is pooled over the stratum (week) and it is impossible to separate out catches according to how many traps are operating.
As for the pooled-Petersen estimator, this will likely result in estimates with low bias, but the precision of the estimates for these strata will be mis-reported, i.e., the standard deviations of the estimated run sizes for these strata will be understated. While there is no way to assess the extent of the problem (other than via simulations), it is hoped that the stratification into weekly strata will resolve most of the underreporting of the precision by the pooled-Petersen estimator and that any remaining understatement is not material.
The two key advantages of the Bayesian approach are:
- accounting for missing data when sampling could not take place
- the self-adjusting performance of the method. If sample sizes are large in each temporal stratum, then very little sharing of information is needed across the strata and very little smoothing of the run distribution is done. However, in case with small sample sizes, more sharing of information across strata occurs and more smoothing is done on the run shape.
Full details are presented in Schwarz and Bonner (2011) and the vignettes of the BTSPAS package.
8.3.4.1 Preliminary screening of the data
A pooled-Petersen estimator would add all of the marked, recaptured and unmarked fish to give an estimate of 1,987,456 (SE 41,322) fish but can the estimate be trusted?
Let us first examine a plot of the estimated capture efficiency at the second trap for each set of releases (Figure 18).
There are several unusual features
- There appears to be heterogeneity in the capture probabilities across the season.
- In some temporal strata, the number of marked fish released and recaptured is very small which lead to estimates with poor precision.
Similarly, let us look at the pattern of unmarked fish captured at the second trap (Figure 19).
The number of unmarked fish captured suddenly jumps by several orders of magnitude (remember the above plot is on the log() scale) in temporal stratum 11. This jump corresponds to releases of hatchery fish into the system.
Finally, let us look at the individual estimates for each stratum found by computing a Petersen estimator for abundance of unmarked fish for each individual stratum (Figure 20).
We see:
- The sudden jumps in abundance due to the hatchery releases is apparent
- There is a fairly regular pattern in abundance with a slow increase until the first hatchery release, followed by a steady decline.
8.3.4.2 Fitting the basic BTSPAS diagonal model
The BTSPAS package attempts to strike a balance between the completely pooled Petersen estimator and the completely stratified Petersen estimator. In the former, capture probabilities are assumed to equal for all fish in all strata, while in the latter, capture probabilities are allowed to vary among strata in no structured way. Furthermore, fish populations often have a general structure to the run, rather than arbitrarily jumping around from stratum to stratum.
The BTSPAS package also has additional features and options:
- the user to use covariates to explain some of the variation in the capture probabilities.
- if \(u_2\) is missing for any stratum, the program will use the spline to interpolate the number of unmarked fish in the population for the missing stratum.
- if \(n_1\) and \(m_2\) are 0, then these strata provide no information towards recapture probabilities. This is useful when no release take place in a stratum (e.g. trap did not run) and so you need ‘dummy’ values as placeholders. Of course if \(n_1>0\) and \(m_2=0\), this provides information that the capture probability may be small. If \(n_1=0\) and \(m_2>0\), this is an error (recoveries from no releases).
- the program allows you specify break points in the underlying spline to account for external events. We was in the above example, that hatchery fish were released at in julian weeks 23 and 40 resulting in sudden jump in abundance. The \(\textit{jump.after}\) parameter gives the julian weeks just BEFORE the sudden jump, i.e. the spline is allowed to jump AFTER the julian weeks in jump.after.
If unfortunate events happen where, for example, no fish could be released, or the second fish wheel is not running in a week, the data should be carefully modified to ensure that missing values are not replaced by 0’s.
The Petersen package function BTSPAS_Diag_fit() is a wrapper to the corresponding function in the BTSPAS package that takes the (modified for bad events) data file, a model for the mean capture probabilities at the second temporal stratum (default is a common mean), and identification of break points in the underlying spline, and then call the function in the BTSPAS package, and formats the returned data structure to match the returning structure for other functions in this package.
If finer control over the fitting process is needed, the BTSPAS package should be called directly – please consult the vignettes that come with the BTSPAS package.
We fit the model”
BTSPAS.diag.fit1 <- Petersen::LP_BTSPAS_fit_Diag(
data_btspas_diag1,
p_model=~1,
jump.after=10,
InitialSeed=23943242
)and look at the summary information on the fit:
The output object contains all of the results and can be saved for later interrogations. This is useful if the run takes considerable time (e.g. overnight) and you want to save the results for later processing.
As noted previously, model comparisons are not easily done using Bayesian methods except for perhaps using DIC (but this is often computed at the incorrect focus of the model). Furthermore, the BTSPAS model are self adjusting and usually the default fit is sufficient.
The final BTSPAS object returned by the fit has many components and contain summary tables, plots, and the the like:
names(BTSPAS.diag.fit1)[1] "summary" "data" "p_model" "p_model_cov" "jump.after"
[6] "InitialSeed" "name_model" "fit" "datetime"
names(BTSPAS.diag.fit1$fit) [1] "n.chains" "n.iter" "n.burnin"
[4] "n.thin" "n.keep" "n.sims"
[7] "sims.array" "sims.list" "sims.matrix"
[10] "summary" "mean" "sd"
[13] "median" "root.short" "long.short"
[16] "dimension.short" "indexes.short" "last.values"
[19] "program" "model.file" "isDIC"
[22] "DICbyR" "pD" "DIC"
[25] "model" "parameters.to.save" "plots"
[28] "runTime" "report" "data"
The plots sub-object contains many plots:
[1] "init.plot" "fit.plot" "logitP.plot"
[4] "acf.Utot.plot" "post.UNtot.plot" "gof.plot"
[7] "trace.logitP.plot" "trace.logU.plot"
In particular, it contains plots of the initial spline fit (init.plot), the final fitted spline (fit.plot), the estimated capture probabilities (on the logit scale) (logitP.plot), plots of the distribution of the posterior sample for the total unmarked and marked fish (post.UNtot.plot) and model diagnostic plots (goodness of fit (gof.plot), trace (trace…plot), and autocorrelation plots (act.Utot.plot).
These plots are all created using the ggplot2 packages, so the user can modify the plot (e.g. change titles etc).
The BTSPAS program also creates a report, which includes information about the data used in the fitting, the pooled- and stratified-Petersen estimates, a test for pooling, and summaries of the posterior. Only the first few lines are shown below:
[1] "Time Stratified Petersen with Diagonal recaptures and error in smoothed U - Mon May 27 20:23:32 2024"
[2] "Version: 2024-05-09 "
[3] ""
[4] ""
[5] ""
[6] " Results "
[7] ""
[8] "*** Raw data *** "
[9] " time n1 m2 u2 logitPcov[1]"
[10] " [1,] 4 1465 51 14587 1"
[11] " [2,] 5 1335 146 2854 1"
[12] " [3,] 6 197 17 1027 1"
[13] " [4,] 7 1335 168 1945 1"
[14] " [5,] 8 1653 72 2855 1"
[15] " [6,] 9 923 43 1323 1"
[16] " [7,] 10 610 28 933 1"
[17] " [8,] 11 7969 297 57549 1"
[18] " [9,] 12 6008 313 14846 1"
[19] "[10,] 13 3770 151 5291 1"
[20] "[11,] 14 4854 309 9249 1"
The fitted spline curve to the number of unmarked fish available in each recovery sample is shown in ?@fig-btspas-diag1-fit-plot
$data
time logUi logU logUlcl logUucl spline
1 4 12.927686 12.858400 12.621356 13.115329 11.546632
2 5 10.164578 10.199596 10.044304 10.357170 10.983029
3 6 9.338304 9.561254 9.152286 10.007612 10.627844
4 7 9.641816 9.673944 9.528708 9.824896 10.392922
5 8 11.078274 11.047969 10.833476 11.274499 10.197187
6 9 10.234017 10.220988 9.956258 10.510632 9.987867
7 10 9.888913 9.874247 9.555136 10.208115 9.719269
8 11 14.246881 14.243708 14.136136 14.358751 14.277170
9 12 12.557340 12.561275 12.454094 12.669492 13.056713
10 13 11.785432 11.783149 11.626268 11.939636 12.029582
11 14 11.883777 11.882899 11.775472 11.995667 11.125502
12 15 10.622351 10.629829 10.533924 10.730142 10.274199
13 16 9.528483 9.553578 9.376165 9.735739 9.405964
14 17 8.241189 8.330916 8.039542 8.631933 8.453353
15 18 6.730651 7.050205 6.533267 7.608104 7.349487
16 19 5.575949 5.942875 5.128041 6.817782 6.027489
$layers
$layers[[1]]
mapping: y = ~logUi
geom_point: na.rm = FALSE
stat_identity: na.rm = FALSE
position_identity
$layers[[2]]
mapping: y = ~logU
geom_point: na.rm = FALSE
stat_identity: na.rm = FALSE
position_identity
$layers[[3]]
mapping: y = ~logU
geom_line: na.rm = FALSE, orientation = NA
stat_identity: na.rm = FALSE
position_identity
$layers[[4]]
mapping: ymin = ~logUlcl, ymax = ~logUucl
geom_errorbar: na.rm = FALSE, orientation = NA, width = 0.1
stat_identity: na.rm = FALSE
position_identity
$layers[[5]]
mapping: y = ~spline
geom_line: na.rm = FALSE, orientation = NA
stat_identity: na.rm = FALSE
position_identity
$scales
<ggproto object: Class ScalesList, gg>
add: function
add_defaults: function
add_missing: function
backtransform_df: function
clone: function
find: function
get_scales: function
has_scale: function
input: function
map_df: function
n: function
non_position_scales: function
scales: list
set_palettes: function
train_df: function
transform_df: function
super: <ggproto object: Class ScalesList, gg>
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<Guides[0] ggproto object>
<empty>
$mapping
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<quosure>
expr: ^time
env: 0x7fc5b38a8298
attr(,"class")
[1] "uneval"
$theme
list()
$coordinates
<ggproto object: Class CoordCartesian, Coord, gg>
aspect: function
backtransform_range: function
clip: on
default: TRUE
distance: function
draw_panel: function
expand: TRUE
is_free: function
is_linear: function
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limits: list
modify_scales: function
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render_axis_h: function
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reverse: none
setup_data: function
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setup_panel_guides: function
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setup_params: function
train_panel_guides: function
transform: function
super: <ggproto object: Class CoordCartesian, Coord, gg>
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<ggproto object: Class FacetNull, Facet, gg>
attach_axes: function
attach_strips: function
compute_layout: function
draw_back: function
draw_front: function
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panel_scales_x: NULL
panel_scales_y: NULL
render: function
render_labels: function
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setup: function
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super: <ggproto object: Class Layout, gg>
$labels
$labels$y
[1] "log(U[i]) + 95% credible interval"
$labels$x
[1] "Time Index\nOpen/closed circles - initial and final estimates"
$labels$title
[1] ""
$labels$subtitle
[1] "Fitted spline curve with 95% credible intervals for estimated log(U[i])"
$labels$ymin
[1] "logUlcl"
$labels$ymax
[1] "logUucl"
attr(,"class")
[1] "gg" "ggplot"
The jump in the spline when hatchery fish are released is evident. The actual number of unmarked fish is allowed to vary around the spline as shown below.
The distribution of the posterior sample for the total number unmarked and total abundance is available as shown in ?@fig-btspas-diag1-postUN
$data
parm sample
1 Utot 2783519
2 Utot 2768535
3 Utot 2699240
4 Utot 2550164
5 Utot 2673304
6 Utot 2836941
7 Utot 2781521
8 Utot 2727428
9 Utot 2479725
10 Utot 2493288
11 Utot 2761439
12 Utot 2800276
13 Utot 2588862
14 Utot 2907390
15 Utot 2860403
16 Utot 2808518
17 Utot 2727836
18 Utot 2834408
19 Utot 2891563
20 Utot 2789477
21 Utot 2761644
22 Utot 2735427
23 Utot 2699897
24 Utot 2750135
25 Utot 2767245
26 Utot 2652881
27 Utot 2622503
28 Utot 2813029
29 Utot 2678718
30 Utot 2699907
31 Utot 2745041
32 Utot 2735805
33 Utot 2819504
34 Utot 2670227
35 Utot 2590954
36 Utot 2774458
37 Utot 2824170
38 Utot 2739734
39 Utot 2914236
40 Utot 2634506
41 Utot 2924845
42 Utot 2830612
43 Utot 2782706
44 Utot 2596148
45 Utot 2738677
46 Utot 2926443
47 Utot 2508027
48 Utot 2654390
49 Utot 2665657
50 Utot 2618884
51 Utot 2720681
52 Utot 2473617
53 Utot 2732428
54 Utot 2809322
55 Utot 2818914
56 Utot 2980773
57 Utot 2839010
58 Utot 2700822
59 Utot 2796278
60 Utot 2875657
61 Utot 2670858
62 Utot 2485682
63 Utot 2794367
64 Utot 2613473
65 Utot 2772038
66 Utot 2752361
67 Utot 2692578
68 Utot 2806932
69 Utot 2684958
70 Utot 2664413
71 Utot 2755502
72 Utot 2846104
73 Utot 2814106
74 Utot 2866886
75 Utot 2818553
76 Utot 2566972
77 Utot 2608723
78 Utot 2773979
79 Utot 2779293
80 Utot 2869542
81 Utot 2722297
82 Utot 2808504
83 Utot 2645385
84 Utot 2746960
85 Utot 2826707
86 Utot 2589867
87 Utot 2785830
88 Utot 2793419
89 Utot 2615393
90 Utot 2705284
91 Utot 2710700
92 Utot 2840347
93 Utot 2635031
94 Utot 2841174
95 Utot 2829757
96 Utot 2689310
97 Utot 2841475
98 Utot 2563537
99 Utot 2702711
100 Utot 2744809
101 Utot 2752633
102 Utot 2901935
103 Utot 2620158
104 Utot 2743359
105 Utot 2650614
106 Utot 2715164
107 Utot 2871801
108 Utot 2645348
109 Utot 2836835
110 Utot 2690552
111 Utot 2774549
112 Utot 2800272
113 Utot 2600724
114 Utot 2685610
115 Utot 2760589
116 Utot 2645236
117 Utot 2469391
118 Utot 2736737
119 Utot 2631140
120 Utot 2819857
121 Utot 2703776
122 Utot 2614727
123 Utot 2724698
124 Utot 2830653
125 Utot 2635688
126 Utot 2829779
127 Utot 2810537
128 Utot 2735091
129 Utot 2654128
130 Utot 2590992
131 Utot 2678034
132 Utot 2563317
133 Utot 2909645
134 Utot 2774493
135 Utot 2887912
136 Utot 2655483
137 Utot 2760335
138 Utot 2692196
139 Utot 2748306
140 Utot 2652051
141 Utot 2740765
142 Utot 2689817
143 Utot 2633003
144 Utot 2749812
145 Utot 2772198
146 Utot 2674679
147 Utot 2637327
148 Utot 2649267
149 Utot 2847512
150 Utot 2695332
151 Utot 2788560
152 Utot 2568017
153 Utot 2838069
154 Utot 2633543
155 Utot 2720079
156 Utot 2818650
157 Utot 2557862
158 Utot 2659965
159 Utot 2713494
160 Utot 2639655
161 Utot 2633698
162 Utot 2625115
163 Utot 2648194
164 Utot 2791566
165 Utot 2478984
166 Utot 2814107
167 Utot 2603648
168 Utot 2736707
169 Utot 2665362
170 Utot 2651430
171 Utot 2802891
172 Utot 2749168
173 Utot 2725972
174 Utot 2900267
175 Utot 2579692
176 Utot 2822909
177 Utot 2629800
178 Utot 2730496
179 Utot 2590638
180 Utot 2614621
181 Utot 2585105
182 Utot 2708589
183 Utot 2873435
184 Utot 2774325
185 Utot 2546845
186 Utot 2884504
187 Utot 2695765
188 Utot 2648814
189 Utot 2855022
190 Utot 2691155
191 Utot 2680015
192 Utot 2591987
193 Utot 2606228
194 Utot 2844293
195 Utot 2709851
196 Utot 2836222
197 Utot 2591797
198 Utot 2673028
199 Utot 2828387
200 Utot 2746360
201 Utot 2754182
202 Utot 2612969
203 Utot 2639064
204 Utot 2728507
205 Utot 2807091
206 Utot 2715870
207 Utot 2719037
208 Utot 2544774
209 Utot 2626019
210 Utot 2440450
211 Utot 2605553
212 Utot 2678174
213 Utot 2781596
214 Utot 2738276
215 Utot 2530347
216 Utot 2590570
217 Utot 2667736
218 Utot 2656669
219 Utot 2673728
220 Utot 2727785
221 Utot 2793254
222 Utot 2627504
223 Utot 2575111
224 Utot 2746400
225 Utot 2845999
226 Utot 2635319
227 Utot 2682882
228 Utot 2768540
229 Utot 2728081
230 Utot 2862987
231 Utot 2832534
232 Utot 2788871
233 Utot 2572813
234 Utot 2633422
235 Utot 2857492
236 Utot 2797289
237 Utot 2819721
238 Utot 2724105
239 Utot 2623643
240 Utot 2740345
241 Utot 2714689
242 Utot 2875365
243 Utot 2719157
244 Utot 2759492
245 Utot 2835710
246 Utot 2838734
247 Utot 2670702
248 Utot 2774787
249 Utot 2801796
250 Utot 2503839
251 Utot 2712191
252 Utot 2713260
253 Utot 2715185
254 Utot 2648538
255 Utot 2897898
256 Utot 2671591
257 Utot 2719840
258 Utot 2681363
259 Utot 2712726
260 Utot 2564976
261 Utot 2777289
262 Utot 2640739
263 Utot 2806004
264 Utot 2692169
265 Utot 2766618
266 Utot 2692840
267 Utot 2725621
268 Utot 3053133
269 Utot 2674725
270 Utot 2756676
271 Utot 2568448
272 Utot 2622331
273 Utot 2683296
274 Utot 2643139
275 Utot 2717427
276 Utot 2696430
277 Utot 2728714
278 Utot 2659228
279 Utot 2859506
280 Utot 2571176
281 Utot 2898701
282 Utot 2630513
283 Utot 2694778
284 Utot 2834354
285 Utot 2853603
286 Utot 2578605
287 Utot 2733628
288 Utot 2753441
289 Utot 2781804
290 Utot 2781795
291 Utot 2829167
292 Utot 2942377
293 Utot 2820857
294 Utot 2540411
295 Utot 2744184
296 Utot 2727833
297 Utot 2607609
298 Utot 2707398
299 Utot 2797922
300 Utot 2775889
301 Utot 2521629
302 Utot 2816656
303 Utot 2805733
304 Utot 2778442
305 Utot 2805254
306 Utot 2880321
307 Utot 2772344
308 Utot 2798063
309 Utot 2506546
310 Utot 2943425
311 Utot 2809345
312 Utot 2542444
313 Utot 2865563
314 Utot 2736915
315 Utot 2675733
316 Utot 2705664
317 Utot 2759516
318 Utot 3058202
319 Utot 2741231
320 Utot 2642324
321 Utot 2911447
322 Utot 2735093
323 Utot 2746212
324 Utot 2999516
325 Utot 2706356
326 Utot 2844612
327 Utot 2575523
328 Utot 2622517
329 Utot 2659609
330 Utot 2920407
331 Utot 2908555
332 Utot 2791410
333 Utot 2841541
334 Utot 2703694
335 Utot 2657963
336 Utot 2744086
337 Utot 2677084
338 Utot 2795191
339 Utot 2701918
340 Utot 2951285
341 Utot 2509567
342 Utot 2602884
343 Utot 2722536
344 Utot 2541620
345 Utot 2792850
346 Utot 2681456
347 Utot 2889582
348 Utot 2956402
349 Utot 2759895
350 Utot 2991825
351 Utot 2732771
352 Utot 2861242
353 Utot 2758053
354 Utot 2959560
355 Utot 2734911
356 Utot 2725880
357 Utot 2740015
358 Utot 2719398
359 Utot 2955417
360 Utot 2737688
361 Utot 2674085
362 Utot 2739614
363 Utot 2708903
364 Utot 2711817
365 Utot 2765098
366 Utot 2712971
367 Utot 2717940
368 Utot 2761580
369 Utot 2551075
370 Utot 2895940
371 Utot 2978321
372 Utot 2838818
373 Utot 2744313
374 Utot 2612781
375 Utot 2837848
376 Utot 2562540
377 Utot 2534089
378 Utot 2748767
379 Utot 2794751
380 Utot 2651684
381 Utot 2811591
382 Utot 2655589
383 Utot 2888873
384 Utot 2734582
385 Utot 2844593
386 Utot 2763113
387 Utot 2726422
388 Utot 2752248
389 Utot 2924283
390 Utot 2707594
391 Utot 2664688
392 Utot 2642596
393 Utot 2831570
394 Utot 2788483
395 Utot 2610476
396 Utot 2546278
397 Utot 2738669
398 Utot 2861935
399 Utot 2712290
400 Utot 2637040
401 Utot 2721966
402 Utot 2609442
403 Utot 2722874
404 Utot 2818463
405 Utot 2746465
406 Utot 2740046
407 Utot 2546684
408 Utot 2627566
409 Utot 2756116
410 Utot 2568649
411 Utot 2770370
412 Utot 2607109
413 Utot 2659871
414 Utot 2796699
415 Utot 2639818
416 Utot 2927436
417 Utot 2603827
418 Utot 2769374
419 Utot 2802169
420 Utot 2716986
421 Utot 2699372
422 Utot 2743245
423 Utot 2562437
424 Utot 2652543
425 Utot 2738379
426 Utot 2658172
427 Utot 2712053
428 Utot 2618233
429 Utot 2630308
430 Utot 2702319
431 Utot 2725751
432 Utot 2769675
433 Utot 2689167
434 Utot 2719632
435 Utot 2743930
436 Utot 2740936
437 Utot 2613207
438 Utot 2712293
439 Utot 2563666
440 Utot 2773978
441 Utot 2813162
442 Utot 2737667
443 Utot 2746990
444 Utot 2505520
445 Utot 2762769
446 Utot 2740422
447 Utot 2754998
448 Utot 2687478
449 Utot 2898301
450 Utot 2617237
451 Utot 2655181
452 Utot 2756671
453 Utot 2845082
454 Utot 2638794
455 Utot 2869514
456 Utot 2674670
457 Utot 2703906
458 Utot 2692872
459 Utot 2658068
460 Utot 3031698
461 Utot 2792989
462 Utot 2587693
463 Utot 2835798
464 Utot 2664455
465 Utot 2707039
466 Utot 2746351
467 Utot 2746430
468 Utot 2774988
469 Utot 2473269
470 Utot 2938598
471 Utot 2587847
472 Utot 2793337
473 Utot 3001432
474 Utot 2577067
475 Utot 2807727
476 Utot 2688282
477 Utot 2615903
478 Utot 2858771
479 Utot 2588140
480 Utot 2639987
481 Utot 2731063
482 Utot 2611338
483 Utot 2641451
484 Utot 2663680
485 Utot 2897577
486 Utot 2809273
487 Utot 2605588
488 Utot 2619449
489 Utot 2663569
490 Utot 2651721
491 Utot 2848835
492 Utot 2710995
493 Utot 2781836
494 Utot 2684485
495 Utot 2716782
496 Utot 2924141
497 Utot 2775463
498 Utot 2843624
499 Utot 2784365
500 Utot 2685169
501 Utot 2761824
502 Utot 2538023
503 Utot 2725733
504 Utot 2707245
505 Utot 2739551
506 Utot 2988699
507 Utot 2834396
508 Utot 2716515
509 Utot 2804982
510 Utot 2681864
511 Utot 2723821
512 Utot 2725364
513 Utot 2747908
514 Utot 2689984
515 Utot 2882851
516 Utot 2555349
517 Utot 2508106
518 Utot 2806437
519 Utot 2725430
520 Utot 2715745
521 Utot 2760572
522 Utot 2592183
523 Utot 2789312
524 Utot 2654374
525 Utot 2744662
526 Utot 2688560
527 Utot 2726679
528 Utot 2668422
529 Utot 3114274
530 Utot 2821195
531 Utot 2879667
532 Utot 2761460
533 Utot 2756258
534 Utot 2694268
535 Utot 2622689
536 Utot 2663886
537 Utot 2762838
538 Utot 2694187
539 Utot 2771909
540 Utot 2794709
541 Utot 2790461
542 Utot 2687814
543 Utot 2790640
544 Utot 2588889
545 Utot 2910538
546 Utot 2608439
547 Utot 2811852
548 Utot 2731425
549 Utot 2669993
550 Utot 2580929
551 Utot 2721727
552 Utot 2719320
553 Utot 2686400
554 Utot 2805196
555 Utot 2619015
556 Utot 2666651
557 Utot 2649665
558 Utot 2625787
559 Utot 2696032
560 Utot 2648736
561 Utot 2659345
562 Utot 2667409
563 Utot 2911537
564 Utot 2796331
565 Utot 2577889
566 Utot 2743011
567 Utot 2664193
568 Utot 2706081
569 Utot 2711713
570 Utot 2668128
571 Utot 2649078
572 Utot 2768723
573 Utot 2789431
574 Utot 2752403
575 Utot 2718062
576 Utot 2739350
577 Utot 2693530
578 Utot 2728200
579 Utot 2653229
580 Utot 2693083
581 Utot 2775900
582 Utot 2685385
583 Utot 2757345
584 Utot 2526737
585 Utot 2872595
586 Utot 2651288
587 Utot 2747147
588 Utot 2595240
589 Utot 2681655
590 Utot 2791830
591 Utot 2655231
592 Utot 2739927
593 Utot 2639482
594 Utot 2557583
595 Utot 2819668
596 Utot 2736194
597 Utot 2742589
598 Utot 2767971
599 Utot 2734595
600 Utot 2675200
601 Utot 2726564
602 Utot 2994640
603 Utot 2768681
604 Utot 2675926
605 Utot 2709409
606 Utot 2716062
607 Utot 2748251
608 Utot 2890888
609 Utot 2695017
610 Utot 2766239
611 Utot 2686783
612 Utot 2642913
613 Utot 2700067
614 Utot 2593920
615 Utot 2697009
616 Utot 2752334
617 Utot 2855546
618 Utot 2866365
619 Utot 2707327
620 Utot 2692177
621 Utot 2606404
622 Utot 2840135
623 Utot 2838272
624 Utot 2531291
625 Utot 2572502
626 Utot 2699691
627 Utot 2663030
628 Utot 2702065
629 Utot 2773914
630 Utot 2490426
631 Utot 2725291
632 Utot 2805568
633 Utot 2743854
634 Utot 2689711
635 Utot 2655466
636 Utot 2797235
637 Utot 2725736
638 Utot 2691050
639 Utot 2640620
640 Utot 2857401
641 Utot 2762911
642 Utot 2773626
643 Utot 2963613
644 Utot 2684399
645 Utot 2647482
646 Utot 2601613
647 Utot 2731418
648 Utot 2694968
649 Utot 2900139
650 Utot 2616384
651 Utot 2575512
652 Utot 2660671
653 Utot 2745173
654 Utot 2812700
655 Utot 2735099
656 Utot 2440536
657 Utot 2835371
658 Utot 2623990
659 Utot 2729543
660 Utot 2818626
661 Utot 2754286
662 Utot 2702967
663 Utot 2720853
664 Utot 2792928
665 Utot 2757558
666 Utot 2756397
667 Utot 2675420
668 Utot 2579046
669 Utot 2732489
670 Utot 2703913
671 Utot 2733122
672 Utot 2761748
673 Utot 2838784
674 Utot 2716467
675 Utot 2827932
676 Utot 2580352
677 Utot 2648209
678 Utot 2720136
679 Utot 2797427
680 Utot 2592549
681 Utot 2732630
682 Utot 2669604
683 Utot 2914978
684 Utot 2748959
685 Utot 2576718
686 Utot 2921848
687 Utot 2874800
688 Utot 2726840
689 Utot 2750613
690 Utot 2836810
691 Utot 2574863
692 Utot 2751083
693 Utot 2822420
694 Utot 2729046
695 Utot 2746890
696 Utot 2627047
697 Utot 2726739
698 Utot 2737343
699 Utot 2650667
700 Utot 2628970
701 Utot 2659927
702 Utot 2636133
703 Utot 2603885
704 Utot 2734570
705 Utot 2799277
706 Utot 2660556
707 Utot 2687590
708 Utot 2835835
709 Utot 2742803
710 Utot 2799048
711 Utot 2739562
712 Utot 2621348
713 Utot 2630038
714 Utot 2770622
715 Utot 2781596
716 Utot 2604785
717 Utot 2818994
718 Utot 2685075
719 Utot 2775334
720 Utot 2613455
721 Utot 2735972
722 Utot 2447622
723 Utot 2657323
724 Utot 2765890
725 Utot 2647660
726 Utot 2671883
727 Utot 2682170
728 Utot 2603798
729 Utot 2594216
730 Utot 2722559
731 Utot 2813928
732 Utot 2764388
733 Utot 2530811
734 Utot 2572123
735 Utot 2608891
736 Utot 2539951
737 Utot 2737024
738 Utot 2786818
739 Utot 2656890
740 Utot 2605167
741 Utot 2632921
742 Utot 2761320
743 Utot 2526413
744 Utot 2533297
745 Utot 2627913
746 Utot 2601555
747 Utot 2553686
748 Utot 2814383
749 Utot 2816368
750 Utot 2663878
751 Utot 2699796
752 Utot 2674059
753 Utot 2698478
754 Utot 2797716
755 Utot 2722025
756 Utot 2688715
757 Utot 2783930
758 Utot 2635557
759 Utot 2806084
760 Utot 2717256
761 Utot 2691305
762 Utot 2640185
763 Utot 2873868
764 Utot 2619651
765 Utot 2642973
766 Utot 2604760
767 Utot 2804125
768 Utot 2732449
769 Utot 2791940
770 Utot 2861565
771 Utot 2620666
772 Utot 2680816
773 Utot 2803238
774 Utot 2980770
775 Utot 2645752
776 Utot 2561312
777 Utot 2663653
778 Utot 2559367
779 Utot 2605444
780 Utot 2559028
781 Utot 2622736
782 Utot 2703081
783 Utot 2672376
784 Utot 2721772
785 Utot 2704394
786 Utot 2614986
787 Utot 2823239
788 Utot 2653151
789 Utot 2687295
790 Utot 2792738
791 Utot 2658551
792 Utot 2764487
793 Utot 2753474
794 Utot 2716073
795 Utot 2676270
796 Utot 2606458
797 Utot 2685341
798 Utot 2761154
799 Utot 2753239
800 Utot 2703805
801 Utot 2777319
802 Utot 2750276
803 Utot 2673896
804 Utot 2808442
805 Utot 2779243
806 Utot 2637753
807 Utot 2846929
808 Utot 2719879
809 Utot 2703813
810 Utot 2804751
811 Utot 2615781
812 Utot 2557913
813 Utot 2817118
814 Utot 2625233
815 Utot 2636704
816 Utot 2626762
817 Utot 2727891
818 Utot 2701889
819 Utot 2622446
820 Utot 2687374
821 Utot 2871030
822 Utot 2604633
823 Utot 2535134
824 Utot 2805896
825 Utot 2803870
826 Utot 2672222
827 Utot 2876827
828 Utot 2739142
829 Utot 2673052
830 Utot 3029574
831 Utot 2838479
832 Utot 2702148
833 Utot 2640214
834 Utot 2814979
835 Utot 2709545
836 Utot 2763024
837 Utot 2556125
838 Utot 2692572
839 Utot 2592922
840 Utot 2519221
841 Utot 2782056
842 Utot 2614749
843 Utot 2684802
844 Utot 2661440
845 Utot 2689565
846 Utot 2771362
847 Utot 2725183
848 Utot 2672290
849 Utot 2681412
850 Utot 2696334
851 Utot 2688234
852 Utot 3035448
853 Utot 2605184
854 Utot 2610177
855 Utot 2693749
856 Utot 2632194
857 Utot 2741388
858 Utot 2670410
859 Utot 2908015
860 Utot 2688281
861 Utot 2762206
862 Utot 2733844
863 Utot 2597293
864 Utot 2710622
865 Utot 2769292
866 Utot 2725935
867 Utot 2669032
868 Utot 2710179
869 Utot 2772491
870 Utot 2833377
871 Utot 2660944
872 Utot 2758309
873 Utot 2719203
874 Utot 2692256
875 Utot 2627238
876 Utot 2689473
877 Utot 2592533
878 Utot 2831656
879 Utot 2757394
880 Utot 2658446
881 Utot 2665646
882 Utot 2695674
883 Utot 2623614
884 Utot 2893201
885 Utot 2607933
886 Utot 2721627
887 Utot 2713850
888 Utot 2631948
889 Utot 2836774
890 Utot 2771797
891 Utot 2533069
892 Utot 2610443
893 Utot 2634268
894 Utot 2663284
895 Utot 2733416
896 Utot 2791393
897 Utot 2599573
898 Utot 2572484
899 Utot 2759789
900 Utot 2823981
901 Utot 2750436
902 Utot 2692924
903 Utot 2697317
904 Utot 2774956
905 Utot 2558331
906 Utot 2671890
907 Utot 2794283
908 Utot 2611580
909 Utot 2723156
910 Utot 2796356
911 Utot 2642858
912 Utot 2679676
913 Utot 2823531
914 Utot 2915499
915 Utot 2586140
916 Utot 2712693
917 Utot 2703569
918 Utot 2813123
919 Utot 2606795
920 Utot 2638689
921 Utot 2847361
922 Utot 2690766
923 Utot 2652620
924 Utot 2743543
925 Utot 2635313
926 Utot 2655544
927 Utot 2804161
928 Utot 2716010
929 Utot 2841021
930 Utot 2784284
931 Utot 2723938
932 Utot 2631852
933 Utot 2759171
934 Utot 2625458
935 Utot 2611780
936 Utot 2834561
937 Utot 2640426
938 Utot 2661580
939 Utot 2707483
940 Utot 2667460
941 Utot 2589555
942 Utot 2790004
943 Utot 2675465
944 Utot 2884643
945 Utot 2771087
946 Utot 2563073
947 Utot 2605676
948 Utot 2619023
949 Utot 2665936
950 Utot 2583872
951 Utot 2645266
952 Utot 2593167
953 Utot 2660101
954 Utot 2626298
955 Utot 2632375
956 Utot 2634633
957 Utot 2790150
958 Utot 2713628
959 Utot 2679419
960 Utot 2844403
961 Utot 2773514
962 Utot 2685304
963 Utot 2726507
964 Utot 2691482
965 Utot 2880687
966 Utot 2697487
967 Utot 2732822
968 Utot 2777626
969 Utot 2841383
970 Utot 2715261
971 Utot 2811906
972 Utot 2694932
973 Utot 2727058
974 Utot 2744995
975 Utot 2582889
976 Utot 2713639
977 Utot 2671855
978 Utot 2672375
979 Utot 2600305
980 Utot 2719403
981 Utot 2734284
982 Utot 2630324
983 Utot 2834995
984 Utot 2735414
985 Utot 2755986
986 Utot 2622765
987 Utot 2837281
988 Utot 2573358
989 Utot 2684667
990 Utot 2613548
991 Utot 2920757
992 Utot 2881721
993 Utot 2690865
994 Utot 2610199
995 Utot 2856814
996 Utot 2719365
997 Utot 2597461
998 Utot 2553726
999 Utot 2783119
1000 Utot 2621186
1001 Utot 2782707
1002 Utot 2906067
1003 Utot 2765012
1004 Utot 2717018
1005 Utot 2690120
1006 Utot 2774637
1007 Utot 2713500
1008 Utot 2705912
1009 Utot 2566167
1010 Utot 2867455
1011 Utot 2614933
1012 Utot 2762378
1013 Utot 2717419
1014 Utot 2787793
1015 Utot 2615637
1016 Utot 2675711
1017 Utot 2748626
1018 Utot 2737252
1019 Utot 2681744
1020 Utot 2694222
1021 Utot 2803846
1022 Utot 2594828
1023 Utot 2628367
1024 Utot 2710938
1025 Utot 2762817
1026 Utot 2781078
1027 Utot 2879257
1028 Utot 2830944
1029 Utot 2736100
1030 Utot 2699324
1031 Utot 2640014
1032 Utot 2712389
1033 Utot 2678587
1034 Utot 2640681
1035 Utot 2999920
1036 Utot 2642502
1037 Utot 2590010
1038 Utot 2513155
1039 Utot 2725713
1040 Utot 2904395
1041 Utot 2768775
1042 Utot 2889818
1043 Utot 2599421
1044 Utot 2778339
1045 Utot 2757319
1046 Utot 2859236
1047 Utot 2630425
1048 Utot 2671414
1049 Utot 2585711
1050 Utot 2774734
1051 Utot 2752727
1052 Utot 2667403
1053 Utot 2769940
1054 Utot 2646004
1055 Utot 2841193
1056 Utot 2713482
1057 Utot 2852160
1058 Utot 2917426
1059 Utot 2642616
1060 Utot 2790668
1061 Utot 2784615
1062 Utot 2781066
1063 Utot 2707892
1064 Utot 2536376
1065 Utot 2739062
1066 Utot 2676557
1067 Utot 2770945
1068 Utot 2763876
1069 Utot 2637530
1070 Utot 2640259
1071 Utot 2772562
1072 Utot 2581730
1073 Utot 2543630
1074 Utot 2578880
1075 Utot 2671259
1076 Utot 2795322
1077 Utot 2712888
1078 Utot 2837163
1079 Utot 2704466
1080 Utot 2586090
1081 Utot 2719744
1082 Utot 2688925
1083 Utot 2640915
1084 Utot 2789929
1085 Utot 2909709
1086 Utot 2774542
1087 Utot 2721026
1088 Utot 2596814
1089 Utot 2684190
1090 Utot 2854748
1091 Utot 2542773
1092 Utot 2712222
1093 Utot 2608983
1094 Utot 2679958
1095 Utot 2580126
1096 Utot 2571913
1097 Utot 2735341
1098 Utot 2561599
1099 Utot 2868800
1100 Utot 2649379
1101 Utot 2870723
1102 Utot 2612035
1103 Utot 2654019
1104 Utot 2879033
1105 Utot 2680378
1106 Utot 2616883
1107 Utot 2702349
1108 Utot 2681738
1109 Utot 2708316
1110 Utot 2651769
1111 Utot 2697358
1112 Utot 2800333
1113 Utot 2589424
1114 Utot 2661461
1115 Utot 2611363
1116 Utot 2706124
1117 Utot 2814099
1118 Utot 2669157
1119 Utot 2760800
1120 Utot 2802714
1121 Utot 2697144
1122 Utot 2697916
1123 Utot 2784447
1124 Utot 2791818
1125 Utot 2567921
1126 Utot 2553930
1127 Utot 2736185
1128 Utot 2853658
1129 Utot 2825334
1130 Utot 2824599
1131 Utot 2822549
1132 Utot 2753195
1133 Utot 2619143
1134 Utot 2861412
1135 Utot 2621632
1136 Utot 2648346
1137 Utot 2803474
1138 Utot 2808799
1139 Utot 2731673
1140 Utot 2796550
1141 Utot 2854289
1142 Utot 2779750
1143 Utot 2785244
1144 Utot 2671388
1145 Utot 2679793
1146 Utot 2693586
1147 Utot 2672576
1148 Utot 2572949
1149 Utot 2566299
1150 Utot 2566708
1151 Utot 2761309
1152 Utot 2860966
1153 Utot 2765523
1154 Utot 2655441
1155 Utot 2856776
1156 Utot 2642410
1157 Utot 2484048
1158 Utot 2982920
1159 Utot 2498278
1160 Utot 2666906
1161 Utot 2579788
1162 Utot 2734207
1163 Utot 2794100
1164 Utot 2840349
1165 Utot 2649073
1166 Utot 2879488
1167 Utot 2861743
1168 Utot 2755762
1169 Utot 2671274
1170 Utot 2677253
1171 Utot 2676568
1172 Utot 2760474
1173 Utot 2646417
1174 Utot 2642596
1175 Utot 2726648
1176 Utot 2886577
1177 Utot 2694508
1178 Utot 2693354
1179 Utot 2755884
1180 Utot 2788087
1181 Utot 2771991
1182 Utot 2561531
1183 Utot 2707972
1184 Utot 2601102
1185 Utot 2718725
1186 Utot 2882122
1187 Utot 2527790
1188 Utot 2684463
1189 Utot 2796497
1190 Utot 2726078
1191 Utot 2729050
1192 Utot 2828951
1193 Utot 2671679
1194 Utot 2672071
1195 Utot 2860630
1196 Utot 2675761
1197 Utot 2547284
1198 Utot 2688398
1199 Utot 2648300
1200 Utot 2960115
1201 Utot 2864113
1202 Utot 2797527
1203 Utot 2594692
1204 Utot 2852663
1205 Utot 2821048
1206 Utot 2522273
1207 Utot 2663676
1208 Utot 2781330
1209 Utot 2835844
1210 Utot 2819631
1211 Utot 2729639
1212 Utot 2706519
1213 Utot 2693895
1214 Utot 2772780
1215 Utot 2589077
1216 Utot 2777358
1217 Utot 2562966
1218 Utot 2699390
1219 Utot 2635368
1220 Utot 2564012
1221 Utot 2882331
1222 Utot 2728383
1223 Utot 2699236
1224 Utot 2665235
1225 Utot 2823614
1226 Utot 2802660
1227 Utot 2784651
1228 Utot 2847771
1229 Utot 2809663
1230 Utot 2878179
1231 Utot 2683148
1232 Utot 2776949
1233 Utot 2923459
1234 Utot 2683320
1235 Utot 2860668
1236 Utot 2650588
1237 Utot 2725559
1238 Utot 2619675
1239 Utot 2794003
1240 Utot 2676633
1241 Utot 2625481
1242 Utot 2746646
1243 Utot 2890844
1244 Utot 2727224
1245 Utot 2569032
1246 Utot 2768491
1247 Utot 2626163
1248 Utot 2649438
1249 Utot 2847159
1250 Utot 2633391
1251 Utot 2599173
1252 Utot 2757536
1253 Utot 2739728
1254 Utot 2447872
1255 Utot 2541370
1256 Utot 2698064
1257 Utot 2712501
1258 Utot 2746210
1259 Utot 2734959
1260 Utot 2516979
1261 Utot 2774912
1262 Utot 2681588
1263 Utot 2701270
1264 Utot 2642403
1265 Utot 2700008
1266 Utot 2895085
1267 Utot 2770360
1268 Utot 2583325
1269 Utot 2814066
1270 Utot 2654499
1271 Utot 2734476
1272 Utot 2768032
1273 Utot 2843354
1274 Utot 2969948
1275 Utot 2885001
1276 Utot 2714438
1277 Utot 2710528
1278 Utot 2718608
1279 Utot 2805583
1280 Utot 2529704
1281 Utot 2822319
1282 Utot 2749519
1283 Utot 2698832
1284 Utot 2820301
1285 Utot 2574938
1286 Utot 2657639
1287 Utot 2645971
1288 Utot 2730090
1289 Utot 2680437
1290 Utot 2699911
1291 Utot 2901624
1292 Utot 2674366
1293 Utot 2589982
1294 Utot 2765038
1295 Utot 2614179
1296 Utot 2502612
1297 Utot 2715141
1298 Utot 2690040
1299 Utot 2774571
1300 Utot 2826367
1301 Utot 2709611
1302 Utot 2783392
1303 Utot 2732913
1304 Utot 2612179
1305 Utot 2848566
1306 Utot 2850001
1307 Utot 2748122
1308 Utot 2697786
1309 Utot 2517011
1310 Utot 2633917
1311 Utot 2533295
1312 Utot 2759204
1313 Utot 2748778
1314 Utot 2731398
1315 Utot 2768623
1316 Utot 2751762
1317 Utot 2643247
1318 Utot 2709318
1319 Utot 2822330
1320 Utot 2619045
1321 Utot 2829759
1322 Utot 2678465
1323 Utot 2572754
1324 Utot 2833800
1325 Utot 2712519
1326 Utot 2749998
1327 Utot 2737609
1328 Utot 2909414
1329 Utot 2616230
1330 Utot 2737961
1331 Utot 2904956
1332 Utot 2848080
1333 Utot 2759412
1334 Utot 2654847
1335 Utot 2629761
1336 Utot 2716412
1337 Utot 2761028
1338 Utot 2640830
1339 Utot 2687599
1340 Utot 2711156
1341 Utot 2759107
1342 Utot 2797330
1343 Utot 2723709
1344 Utot 2791002
1345 Utot 2736473
1346 Utot 2533291
1347 Utot 2736725
1348 Utot 2726514
1349 Utot 2692668
1350 Utot 2653469
1351 Utot 2738486
1352 Utot 2660038
1353 Utot 2711538
1354 Utot 2663420
1355 Utot 2702513
1356 Utot 2782729
1357 Utot 2910143
1358 Utot 2701917
1359 Utot 2768613
1360 Utot 2681231
1361 Utot 2645869
1362 Utot 2640981
1363 Utot 2389651
1364 Utot 2858249
1365 Utot 2731575
1366 Utot 2578556
1367 Utot 2735423
1368 Utot 2683964
1369 Utot 2758507
1370 Utot 2753115
1371 Utot 2703976
1372 Utot 2847807
1373 Utot 2790198
1374 Utot 2765709
1375 Utot 2702315
1376 Utot 2930540
1377 Utot 2744489
1378 Utot 2833607
1379 Utot 2956830
1380 Utot 2756526
1381 Utot 2601802
1382 Utot 2573561
1383 Utot 2626927
1384 Utot 3037060
1385 Utot 2791004
1386 Utot 2616883
1387 Utot 2572597
1388 Utot 2813842
1389 Utot 2650666
1390 Utot 2852644
1391 Utot 2613794
1392 Utot 2707445
1393 Utot 2644964
1394 Utot 2794656
1395 Utot 3101603
1396 Utot 2711153
1397 Utot 2889634
1398 Utot 2679920
1399 Utot 2729094
1400 Utot 2757651
1401 Utot 2776005
1402 Utot 2716015
1403 Utot 2725444
1404 Utot 2709070
1405 Utot 2671975
1406 Utot 2699077
1407 Utot 2589194
1408 Utot 2910277
1409 Utot 2691390
1410 Utot 2559677
1411 Utot 2621803
1412 Utot 2683984
1413 Utot 2675155
1414 Utot 2712232
1415 Utot 2643903
1416 Utot 2708605
1417 Utot 2736018
1418 Utot 2724708
1419 Utot 2730726
1420 Utot 2710453
1421 Utot 2757003
1422 Utot 2616363
1423 Utot 2670249
1424 Utot 2675081
1425 Utot 2692561
1426 Utot 2748827
1427 Utot 2660624
1428 Utot 2609929
1429 Utot 2680679
1430 Utot 2781769
1431 Utot 2623594
1432 Utot 2768360
1433 Utot 2769849
1434 Utot 2713819
1435 Utot 2771275
1436 Utot 2685018
1437 Utot 2763254
1438 Utot 2611786
1439 Utot 2556039
1440 Utot 2666782
1441 Utot 2749918
1442 Utot 2652510
1443 Utot 2699961
1444 Utot 2667917
1445 Utot 2703314
1446 Utot 2699212
1447 Utot 2696541
1448 Utot 2947295
1449 Utot 2628995
1450 Utot 2775040
1451 Utot 2776289
1452 Utot 2809517
1453 Utot 2636971
1454 Utot 2674182
1455 Utot 2771956
1456 Utot 2735185
1457 Utot 2732219
1458 Utot 2575494
1459 Utot 2680598
1460 Utot 2724722
1461 Utot 2611851
1462 Utot 2608154
1463 Utot 2747334
1464 Utot 2715143
1465 Utot 2841535
1466 Utot 2727142
1467 Utot 2853284
1468 Utot 2833242
1469 Utot 2594636
1470 Utot 2876316
1471 Utot 2772278
1472 Utot 2653611
1473 Utot 2676026
1474 Utot 2803461
1475 Utot 2703552
1476 Utot 2780094
1477 Utot 2668077
1478 Utot 2618831
1479 Utot 2782523
1480 Utot 2779751
1481 Utot 2524955
1482 Utot 2810648
1483 Utot 2716226
1484 Utot 2753664
1485 Utot 2668324
1486 Utot 2683354
1487 Utot 2648993
1488 Utot 2778556
1489 Utot 2745440
1490 Utot 2843569
1491 Utot 2759316
1492 Utot 2663548
1493 Utot 2748276
1494 Utot 2606812
1495 Utot 2774526
1496 Utot 2672921
1497 Utot 2680534
1498 Utot 2774114
1499 Utot 2650267
1500 Utot 2695650
1501 Utot 2680660
1502 Utot 2553337
1503 Utot 2730033
1504 Utot 2729534
1505 Utot 2682071
1506 Utot 2945241
1507 Utot 2773416
1508 Utot 2760178
1509 Utot 2758483
1510 Utot 2711416
1511 Utot 2629579
1512 Utot 2500501
1513 Utot 2610700
1514 Utot 2894469
1515 Utot 2671683
1516 Utot 2747213
1517 Utot 2839895
1518 Utot 2777614
1519 Utot 2629341
1520 Utot 2663151
1521 Utot 2787212
1522 Utot 2572436
1523 Utot 2751313
1524 Utot 2863662
1525 Utot 2911238
1526 Utot 2531116
1527 Utot 2629151
1528 Utot 2747015
1529 Utot 2906253
1530 Utot 2703041
1531 Utot 2674498
1532 Utot 2962241
1533 Utot 2633038
1534 Utot 2728204
1535 Utot 2598234
1536 Utot 2628579
1537 Utot 3009772
1538 Utot 2804393
1539 Utot 2604599
1540 Utot 2578533
1541 Utot 2781240
1542 Utot 2718145
1543 Utot 2751242
1544 Utot 2632138
1545 Utot 2554579
1546 Utot 2639434
1547 Utot 2783704
1548 Utot 2744540
1549 Utot 2836119
1550 Utot 2998366
1551 Utot 2867746
1552 Utot 2679020
1553 Utot 2723492
1554 Utot 2641747
1555 Utot 2819355
1556 Utot 2910906
1557 Utot 2498691
1558 Utot 2755892
1559 Utot 2685973
1560 Utot 2644928
1561 Utot 2570537
1562 Utot 2854226
1563 Utot 2939295
1564 Utot 2828663
1565 Utot 2749502
1566 Utot 2828399
1567 Utot 2721734
1568 Utot 2513473
1569 Utot 2649024
1570 Utot 2511528
1571 Utot 2655852
1572 Utot 2664146
1573 Utot 2606301
1574 Utot 2908433
1575 Utot 2765314
1576 Utot 2815222
1577 Utot 2845649
1578 Utot 2691833
1579 Utot 2796566
1580 Utot 2599650
1581 Utot 2610228
1582 Utot 2766635
1583 Utot 2682130
1584 Utot 2699205
1585 Utot 2555242
1586 Utot 2715513
1587 Utot 2781164
1588 Utot 2592845
1589 Utot 2692782
1590 Utot 2823479
1591 Utot 2741073
1592 Utot 2837625
1593 Utot 2909557
1594 Utot 2613788
1595 Utot 2776452
1596 Utot 2644169
1597 Utot 2711153
1598 Utot 2641683
1599 Utot 2801062
1600 Utot 2993621
1601 Utot 2591001
1602 Utot 2653930
1603 Utot 2632677
1604 Utot 2531391
1605 Utot 2664199
1606 Utot 2693084
1607 Utot 2713631
1608 Utot 2722273
1609 Utot 2755456
1610 Utot 2811611
1611 Utot 2770482
1612 Utot 2520313
1613 Utot 2641281
1614 Utot 2620716
1615 Utot 2564233
1616 Utot 2458695
1617 Utot 2946641
1618 Utot 2738446
1619 Utot 2718660
1620 Utot 2831836
1621 Utot 2663533
1622 Utot 2605974
1623 Utot 2684080
1624 Utot 2751305
1625 Utot 2659870
1626 Utot 2575451
1627 Utot 2761707
1628 Utot 2700873
1629 Utot 2954476
1630 Utot 2832939
1631 Utot 2625844
1632 Utot 2714497
1633 Utot 2710313
1634 Utot 2934566
1635 Utot 2800004
1636 Utot 2576912
1637 Utot 2715317
1638 Utot 2850789
1639 Utot 2672866
1640 Utot 2566278
1641 Utot 2805910
1642 Utot 2585412
1643 Utot 2537554
1644 Utot 2739513
1645 Utot 2837200
1646 Utot 2786017
1647 Utot 2669354
1648 Utot 2793109
1649 Utot 2881405
1650 Utot 2500405
1651 Utot 2667648
1652 Utot 2801891
1653 Utot 2640043
1654 Utot 2753281
1655 Utot 2782892
1656 Utot 2933772
1657 Utot 2776186
1658 Utot 2688982
1659 Utot 2908287
1660 Utot 2874343
1661 Utot 2794246
1662 Utot 2909658
1663 Utot 2697865
1664 Utot 2766284
1665 Utot 2670462
1666 Utot 2653684
1667 Utot 2559489
1668 Utot 2569431
1669 Utot 2741758
1670 Utot 2736855
1671 Utot 2836102
1672 Utot 2769806
1673 Utot 2696758
1674 Utot 2811447
1675 Utot 2690707
1676 Utot 2806887
1677 Utot 2683600
1678 Utot 2574376
1679 Utot 2787573
1680 Utot 2789589
1681 Utot 2716612
1682 Utot 2754070
1683 Utot 2844339
1684 Utot 2692575
1685 Utot 2806811
1686 Utot 2636655
1687 Utot 2782008
1688 Utot 2695010
1689 Utot 2594214
1690 Utot 2790097
1691 Utot 2817388
1692 Utot 2618558
1693 Utot 2795000
1694 Utot 2896239
1695 Utot 2723578
1696 Utot 2716016
1697 Utot 2716912
1698 Utot 2945536
1699 Utot 2752031
1700 Utot 2437306
1701 Utot 2843376
1702 Utot 2884751
1703 Utot 2605394
1704 Utot 2629481
1705 Utot 2578346
1706 Utot 2737036
1707 Utot 2887282
1708 Utot 2858476
1709 Utot 2636782
1710 Utot 2718250
1711 Utot 2683569
1712 Utot 2487812
1713 Utot 2611931
1714 Utot 2595328
1715 Utot 2693095
1716 Utot 2829258
1717 Utot 2523665
1718 Utot 2663074
1719 Utot 2841848
1720 Utot 2869253
1721 Utot 2711843
1722 Utot 2788557
1723 Utot 2681930
1724 Utot 2743825
1725 Utot 2565601
1726 Utot 2717773
1727 Utot 2749776
1728 Utot 2664384
1729 Utot 2752240
1730 Utot 2636332
1731 Utot 2884302
1732 Utot 2749275
1733 Utot 2800360
1734 Utot 2746395
1735 Utot 2780902
1736 Utot 2772717
1737 Utot 2653113
1738 Utot 2770142
1739 Utot 2552497
1740 Utot 2666634
1741 Utot 2729409
1742 Utot 2702461
1743 Utot 2743738
1744 Utot 2729636
1745 Utot 2714248
1746 Utot 2697568
1747 Utot 2678019
1748 Utot 2789026
1749 Utot 2734263
1750 Utot 2789426
1751 Utot 2682675
1752 Utot 2660709
1753 Utot 2578947
1754 Utot 2813924
1755 Utot 2844703
1756 Utot 2597286
1757 Utot 2635758
1758 Utot 2739452
1759 Utot 2779755
1760 Utot 2655328
1761 Utot 2859485
1762 Utot 2862108
1763 Utot 2610686
1764 Utot 2746785
1765 Utot 2682447
1766 Utot 2716657
1767 Utot 2612928
1768 Utot 2618021
1769 Utot 2511231
1770 Utot 2604866
1771 Utot 2914113
1772 Utot 2789269
1773 Utot 2636884
1774 Utot 2674174
1775 Utot 2759610
1776 Utot 2643381
1777 Utot 2791936
1778 Utot 2634035
1779 Utot 2915627
1780 Utot 2849606
1781 Utot 2785549
1782 Utot 2845017
1783 Utot 2736770
1784 Utot 2845219
1785 Utot 2686325
1786 Utot 2804350
1787 Utot 2658959
1788 Utot 2644622
1789 Utot 2652758
1790 Utot 2571552
1791 Utot 2811673
1792 Utot 2714296
1793 Utot 2675044
1794 Utot 2716344
1795 Utot 2761917
1796 Utot 2549079
1797 Utot 2686105
1798 Utot 2562072
1799 Utot 2571748
1800 Utot 2642144
1801 Utot 2646580
1802 Utot 2641923
1803 Utot 2660298
1804 Utot 2679886
1805 Utot 2621781
1806 Utot 2814883
1807 Utot 2707216
1808 Utot 2670873
1809 Utot 2740217
1810 Utot 2646420
1811 Utot 2600724
1812 Utot 2609570
1813 Utot 2905255
1814 Utot 2759255
1815 Utot 2616924
1816 Utot 2557798
1817 Utot 2720589
1818 Utot 2758976
1819 Utot 2656530
1820 Utot 2720216
1821 Utot 2821877
1822 Utot 2565219
1823 Utot 2500885
1824 Utot 2828940
1825 Utot 2711854
1826 Utot 2655415
1827 Utot 2805182
1828 Utot 2725663
1829 Utot 2693375
1830 Utot 2662636
1831 Utot 2693014
1832 Utot 3007542
1833 Utot 2674425
1834 Utot 2750687
1835 Utot 2816609
1836 Utot 2594412
1837 Utot 2679040
1838 Utot 2854454
1839 Utot 2618128
1840 Utot 2733112
1841 Utot 2754926
1842 Utot 2556736
1843 Utot 2939158
1844 Utot 2741680
1845 Utot 2653188
1846 Utot 2687671
1847 Utot 2674441
1848 Utot 2740106
1849 Utot 2683898
1850 Utot 2655605
1851 Utot 2767277
1852 Utot 2924219
1853 Utot 2679756
1854 Utot 2717430
1855 Utot 2749761
1856 Utot 2756332
1857 Utot 2729466
1858 Utot 2728913
1859 Utot 2857429
1860 Utot 2606062
1861 Utot 2823973
1862 Utot 2542353
1863 Utot 2707638
1864 Utot 2753117
1865 Utot 2826868
1866 Utot 2564222
1867 Utot 2761238
1868 Utot 2616217
1869 Utot 2569738
1870 Utot 2554043
1871 Utot 2575608
1872 Utot 2831033
1873 Utot 2573625
1874 Utot 2787128
1875 Utot 2871082
1876 Utot 2825511
1877 Utot 2678645
1878 Utot 2740136
1879 Utot 2791367
1880 Utot 2734092
1881 Utot 2646968
1882 Utot 2665062
1883 Utot 2726753
1884 Utot 2816517
1885 Utot 2538974
1886 Utot 2728535
1887 Utot 2580194
1888 Utot 2645241
1889 Utot 2670353
1890 Utot 2560745
1891 Utot 2846191
1892 Utot 2741914
1893 Utot 2636238
1894 Utot 2575106
1895 Utot 2851903
1896 Utot 2718687
1897 Utot 2690098
1898 Utot 2850972
1899 Utot 2849673
1900 Utot 2716342
1901 Utot 2725190
1902 Utot 2815922
1903 Utot 2790598
1904 Utot 2724719
1905 Utot 2728506
1906 Utot 2689294
1907 Utot 2870109
1908 Utot 2650174
1909 Utot 2699620
1910 Utot 2688370
1911 Utot 2725093
1912 Utot 2782565
1913 Utot 2711719
1914 Utot 2862479
1915 Utot 2636436
1916 Utot 2666805
1917 Utot 2835402
1918 Utot 2637899
1919 Utot 2648389
1920 Utot 2831154
1921 Utot 2696415
1922 Utot 2698216
1923 Utot 2555553
1924 Utot 2639891
1925 Utot 2604973
1926 Utot 2741001
1927 Utot 2676941
1928 Utot 2706446
1929 Utot 2783256
1930 Utot 2871178
1931 Utot 2755430
1932 Utot 2579214
1933 Utot 2905312
1934 Utot 2691451
1935 Utot 2933768
1936 Utot 2652010
1937 Utot 2532616
1938 Utot 2848383
1939 Utot 2635176
1940 Utot 2767918
1941 Utot 2874186
1942 Utot 2615063
1943 Utot 2673746
1944 Utot 2843736
1945 Utot 2656725
1946 Utot 2750187
1947 Utot 2648911
1948 Utot 2644750
1949 Utot 2671788
1950 Utot 2742223
1951 Utot 2772575
1952 Utot 2770755
1953 Utot 2787398
1954 Utot 2650310
1955 Utot 2620291
1956 Utot 3056794
1957 Utot 2563551
1958 Utot 2623431
1959 Utot 2864035
1960 Utot 2735055
1961 Utot 2736902
1962 Utot 2652644
1963 Utot 2741653
1964 Utot 2604568
1965 Utot 2789399
1966 Utot 2748088
1967 Utot 2529036
1968 Utot 2801127
1969 Utot 2709181
1970 Utot 2643391
1971 Utot 2671117
1972 Utot 2651378
1973 Utot 2715502
1974 Utot 2911756
1975 Utot 2700615
1976 Utot 2941183
1977 Utot 2702992
1978 Utot 2624649
1979 Utot 2634436
1980 Utot 2768680
1981 Utot 2690870
1982 Utot 2822514
1983 Utot 2666195
1984 Utot 2791015
1985 Utot 3042266
1986 Utot 2812080
1987 Utot 2619247
1988 Utot 2618086
1989 Utot 2706485
1990 Utot 2589216
1991 Utot 2820198
1992 Utot 2584964
1993 Utot 2564119
1994 Utot 2582746
1995 Utot 2757064
1996 Utot 2661302
1997 Utot 2854171
1998 Utot 2681309
1999 Utot 2817207
2000 Utot 2848094
2001 Utot 2668605
2002 Utot 2634757
2003 Utot 2817934
2004 Utot 2870783
2005 Utot 2595966
2006 Utot 2784124
2007 Utot 2595905
2008 Utot 2628936
2009 Utot 2798237
2010 Utot 2619998
2011 Utot 2767268
2012 Utot 2702249
2013 Utot 2712169
2014 Utot 2540839
2015 Utot 2709191
2016 Utot 2758570
2017 Utot 2568968
2018 Utot 2748978
2019 Utot 2622829
2020 Utot 2529340
2021 Utot 2713228
2022 Utot 2764860
2023 Utot 2628822
2024 Utot 2750688
2025 Utot 2677973
2026 Utot 2581024
2027 Utot 2744319
2028 Utot 2716369
2029 Utot 2723575
2030 Utot 2804569
2031 Utot 2929754
2032 Utot 2874607
2033 Utot 2677316
2034 Utot 2652633
2035 Utot 3074159
2036 Utot 2637920
2037 Utot 2733925
2038 Utot 2692529
2039 Utot 2668612
2040 Utot 2735525
2041 Utot 2605617
2042 Utot 2533534
2043 Utot 2642236
2044 Utot 2703661
2045 Utot 2953811
2046 Utot 2592783
2047 Utot 2655246
2048 Utot 2598602
2049 Utot 2692239
2050 Utot 2796200
2051 Utot 2831180
2052 Utot 2604991
2053 Utot 2801416
2054 Utot 2514753
2055 Utot 2685714
2056 Utot 2708464
2057 Utot 2555196
2058 Utot 2620249
2059 Utot 2594201
2060 Utot 2703761
2061 Utot 2865142
2062 Utot 2831270
2063 Utot 2700623
2064 Utot 2533871
2065 Utot 2793681
2066 Utot 2766637
2067 Utot 2958199
2068 Utot 2812864
2069 Utot 2744563
2070 Utot 2767518
2071 Utot 2566547
2072 Utot 2652553
2073 Utot 2710625
2074 Utot 2798974
2075 Utot 2726281
2076 Utot 2676549
2077 Utot 2849667
2078 Utot 2716990
2079 Utot 2703505
2080 Utot 2481169
2081 Utot 2507903
2082 Utot 2905720
2083 Utot 2622199
2084 Utot 2683098
2085 Utot 2555104
2086 Utot 2648093
2087 Utot 2785802
2088 Utot 2667010
2089 Utot 2642264
2090 Utot 2621734
2091 Utot 2661404
2092 Utot 2673627
2093 Utot 2591994
2094 Utot 2899894
2095 Utot 2678450
2096 Utot 2757666
2097 Utot 2845513
2098 Utot 2627585
2099 Utot 2609397
2100 Utot 2725542
2101 Utot 2858588
2102 Utot 2731461
2103 Utot 2671558
2104 Utot 2604908
2105 Utot 2806542
2106 Utot 2824846
2107 Utot 2788120
2108 Utot 2806719
2109 Utot 2748110
2110 Utot 2795465
2111 Utot 2579013
2112 Utot 2572743
2113 Utot 2637939
2114 Utot 2712953
2115 Utot 2736445
2116 Utot 2600479
2117 Utot 2706977
2118 Utot 2795664
2119 Utot 2591863
2120 Utot 2600552
2121 Utot 2754832
2122 Utot 2606482
2123 Utot 2675618
2124 Utot 2629515
2125 Utot 2584161
2126 Utot 2688842
2127 Utot 2763201
2128 Utot 2729604
2129 Utot 2650231
2130 Utot 2567382
2131 Utot 2731121
2132 Utot 2497591
2133 Utot 2689664
2134 Utot 2667384
2135 Utot 2625422
2136 Utot 2768132
2137 Utot 2886848
2138 Utot 2717615
2139 Utot 2952202
2140 Utot 2609366
2141 Utot 2657387
2142 Utot 2759904
2143 Utot 2840618
2144 Utot 2639545
2145 Utot 2821023
2146 Utot 2667490
2147 Utot 2844918
2148 Utot 2739274
2149 Utot 2738313
2150 Utot 2743837
2151 Utot 2775548
2152 Utot 2721266
2153 Utot 2650860
2154 Utot 2558957
2155 Utot 2847603
2156 Utot 2692949
2157 Utot 2818087
2158 Utot 2820770
2159 Utot 2949927
2160 Utot 2897114
2161 Utot 2778256
2162 Utot 2983835
2163 Utot 2575631
2164 Utot 2740113
2165 Utot 2606772
2166 Utot 2705658
2167 Utot 2813376
2168 Utot 2781340
2169 Utot 2592517
2170 Utot 2619402
2171 Utot 2809643
2172 Utot 2867526
2173 Utot 2872345
2174 Utot 2779385
2175 Utot 2876773
2176 Utot 2536869
2177 Utot 2622561
2178 Utot 2967036
2179 Utot 2738026
2180 Utot 2517509
2181 Utot 2653877
2182 Utot 2733731
2183 Utot 2728329
2184 Utot 2739528
2185 Utot 2524749
2186 Utot 2749248
2187 Utot 2525207
2188 Utot 2654240
2189 Utot 2643343
2190 Utot 2675290
2191 Utot 2693342
2192 Utot 2744487
2193 Utot 2885365
2194 Utot 2640619
2195 Utot 2557542
2196 Utot 2895407
2197 Utot 2667313
2198 Utot 2672186
2199 Utot 2632964
2200 Utot 2715920
2201 Utot 2587272
2202 Utot 2739563
2203 Utot 2708114
2204 Utot 2654514
2205 Utot 2683900
2206 Utot 2729902
2207 Utot 2587012
2208 Utot 2762713
2209 Utot 2903069
2210 Utot 2690056
2211 Utot 2881401
2212 Utot 2854886
2213 Utot 2814565
2214 Utot 2741426
2215 Utot 2627501
2216 Utot 2742821
2217 Utot 2658141
2218 Utot 2888536
2219 Utot 2697909
2220 Utot 2627362
2221 Utot 2697493
2222 Utot 2788092
2223 Utot 2787775
2224 Utot 2793008
2225 Utot 2814317
2226 Utot 2806419
2227 Utot 2698337
2228 Utot 2790558
2229 Utot 2823931
2230 Utot 2511388
2231 Utot 2538872
2232 Utot 2766877
2233 Utot 2645796
2234 Utot 2717142
2235 Utot 2672864
2236 Utot 2852797
2237 Utot 2687380
2238 Utot 2601798
2239 Utot 2535403
2240 Utot 2651812
2241 Utot 2584347
2242 Utot 2777666
2243 Utot 2685249
2244 Utot 2632154
2245 Utot 2797364
2246 Utot 2778156
2247 Utot 2816978
2248 Utot 2620807
2249 Utot 2762967
2250 Utot 2800822
2251 Utot 2606535
2252 Utot 2388322
2253 Utot 2676296
2254 Utot 2640688
2255 Utot 2730058
2256 Utot 2643200
2257 Utot 2850177
2258 Utot 2640647
2259 Utot 2785945
2260 Utot 2847582
2261 Utot 2668331
2262 Utot 2697474
2263 Utot 2743064
2264 Utot 2586363
2265 Utot 2679263
2266 Utot 2623268
2267 Utot 2874471
2268 Utot 2785456
2269 Utot 2915700
2270 Utot 2652769
2271 Utot 2709957
2272 Utot 2601138
2273 Utot 2862046
2274 Utot 2886374
2275 Utot 2562326
2276 Utot 2783806
2277 Utot 2839032
2278 Utot 2775269
2279 Utot 2780764
2280 Utot 2632741
2281 Utot 2600705
2282 Utot 2575929
2283 Utot 2733212
2284 Utot 2532028
2285 Utot 2868394
2286 Utot 2724944
2287 Utot 2714006
2288 Utot 2665169
2289 Utot 2606712
2290 Utot 2706541
2291 Utot 2846886
2292 Utot 3026557
2293 Utot 2596426
2294 Utot 2911183
2295 Utot 2567862
2296 Utot 2679213
2297 Utot 2700551
2298 Utot 2677322
2299 Utot 2900670
2300 Utot 2612738
2301 Utot 2840109
2302 Utot 2704271
2303 Utot 2738579
2304 Utot 2824526
2305 Utot 2609107
2306 Utot 2623448
2307 Utot 2765000
2308 Utot 2793433
2309 Utot 2712562
2310 Utot 2675122
2311 Utot 2992781
2312 Utot 2836735
2313 Utot 2790773
2314 Utot 2790058
2315 Utot 2572930
2316 Utot 2849347
2317 Utot 2702428
2318 Utot 2758444
2319 Utot 2783985
2320 Utot 2529246
2321 Utot 2507747
2322 Utot 2804787
2323 Utot 2854441
2324 Utot 2823417
2325 Utot 2782106
2326 Utot 2658891
2327 Utot 2650127
2328 Utot 2580670
2329 Utot 2748178
2330 Utot 2658156
2331 Utot 2749607
2332 Utot 2716384
2333 Utot 2688070
2334 Utot 2673886
2335 Utot 2965267
2336 Utot 2652761
2337 Utot 2555021
2338 Utot 2717578
2339 Utot 2768741
2340 Utot 2619342
2341 Utot 2646736
2342 Utot 2887680
2343 Utot 2678758
2344 Utot 2620950
2345 Utot 2761298
2346 Utot 2768840
2347 Utot 2733012
2348 Utot 2586263
2349 Utot 2645489
2350 Utot 2618985
2351 Utot 2700532
2352 Utot 2763961
2353 Utot 2747050
2354 Utot 2720257
2355 Utot 2775708
2356 Utot 2861110
2357 Utot 2690756
2358 Utot 2721066
2359 Utot 2625466
2360 Utot 2627384
2361 Utot 2739160
2362 Utot 2580727
2363 Utot 2691848
2364 Utot 2647465
2365 Utot 2779433
2366 Utot 2691391
2367 Utot 2740828
2368 Utot 2835045
2369 Utot 2863075
2370 Utot 2779002
2371 Utot 2663080
2372 Utot 2817170
2373 Utot 2706877
2374 Utot 2703716
2375 Utot 2685125
2376 Utot 2751803
2377 Utot 2674832
2378 Utot 2914303
2379 Utot 2654738
2380 Utot 2755223
2381 Utot 2882396
2382 Utot 2758707
2383 Utot 2696210
2384 Utot 2787818
2385 Utot 2778790
2386 Utot 2599223
2387 Utot 2678143
2388 Utot 2636270
2389 Utot 2653722
2390 Utot 2547172
2391 Utot 2672596
2392 Utot 2678364
2393 Utot 2578704
2394 Utot 2885880
2395 Utot 2691165
2396 Utot 2888530
2397 Utot 2730189
2398 Utot 2746429
2399 Utot 2802620
2400 Utot 2727410
2401 Utot 2780405
2402 Utot 2768444
2403 Utot 2799563
2404 Utot 2679547
2405 Utot 2786595
2406 Utot 2733150
2407 Utot 2874854
2408 Utot 2816972
2409 Utot 2630326
2410 Utot 2954665
2411 Utot 2746787
2412 Utot 2857446
2413 Utot 2608465
2414 Utot 2799308
2415 Utot 2523242
2416 Utot 2661204
2417 Utot 2698203
2418 Utot 2721619
2419 Utot 2768779
2420 Utot 2743806
2421 Utot 2779235
2422 Utot 2651117
2423 Utot 2561187
2424 Utot 2731286
2425 Utot 2693790
2426 Utot 2666409
2427 Utot 2802567
2428 Utot 2764144
2429 Utot 2722855
2430 Utot 2771478
2431 Utot 2608106
2432 Utot 2769923
2433 Utot 2618965
2434 Utot 2615350
2435 Utot 2732487
2436 Utot 2730044
2437 Utot 2539737
2438 Utot 2894850
2439 Utot 2736328
2440 Utot 2785613
2441 Utot 2483593
2442 Utot 2816599
2443 Utot 2441692
2444 Utot 2766703
2445 Utot 2773198
2446 Utot 2683575
2447 Utot 2731689
2448 Utot 2588074
2449 Utot 2699544
2450 Utot 2692808
2451 Utot 2917482
2452 Utot 2580806
2453 Utot 2742418
2454 Utot 2618875
2455 Utot 2619990
2456 Utot 2846977
2457 Utot 2940935
2458 Utot 2778213
2459 Utot 2787270
2460 Utot 2646994
2461 Utot 2571836
2462 Utot 2762082
2463 Utot 2805537
2464 Utot 2678165
2465 Utot 2995841
2466 Utot 2563230
2467 Utot 2797767
2468 Utot 2787970
2469 Utot 2576427
2470 Utot 2709344
2471 Utot 2689881
2472 Utot 2613630
2473 Utot 2713009
2474 Utot 2766959
2475 Utot 2698604
2476 Utot 2566839
2477 Utot 2705512
2478 Utot 2831226
2479 Utot 2892693
2480 Utot 2731789
2481 Utot 2659102
2482 Utot 2595254
2483 Utot 2859281
2484 Utot 2644746
2485 Utot 2661618
2486 Utot 2573152
2487 Utot 2695357
2488 Utot 2591076
2489 Utot 2650672
2490 Utot 2684322
2491 Utot 3034981
2492 Utot 2764615
2493 Utot 2682304
2494 Utot 2812895
2495 Utot 2600769
2496 Utot 2694041
2497 Utot 2886393
2498 Utot 2800144
2499 Utot 2780959
2500 Utot 2671246
2501 Utot 2623255
2502 Utot 2698177
2503 Utot 2801033
2504 Utot 2609393
2505 Utot 2804069
2506 Utot 2714114
2507 Utot 2733317
2508 Utot 2541450
2509 Utot 2777008
2510 Utot 2809334
2511 Utot 2835419
2512 Utot 2562444
2513 Utot 2725996
2514 Utot 2661421
2515 Utot 2709708
2516 Utot 2864272
2517 Utot 2941401
2518 Utot 2686392
2519 Utot 2650740
2520 Utot 2746667
2521 Utot 2567673
2522 Utot 2672044
2523 Utot 2728318
2524 Utot 2709813
2525 Utot 2676451
2526 Utot 2573334
2527 Utot 2539195
2528 Utot 2625506
2529 Utot 2899930
2530 Utot 2657016
2531 Utot 2698606
2532 Utot 2949088
2533 Utot 2617557
2534 Utot 2736963
2535 Utot 2766554
2536 Utot 2723747
2537 Utot 2791480
2538 Utot 2722524
2539 Utot 2758820
2540 Utot 2642888
2541 Utot 2740356
2542 Utot 2707167
2543 Utot 2887974
2544 Utot 2787113
2545 Utot 2719464
2546 Utot 2815437
2547 Utot 2751105
2548 Utot 2700975
2549 Utot 2621514
2550 Utot 2629273
2551 Utot 2804782
2552 Utot 2775784
2553 Utot 2721673
2554 Utot 2577363
2555 Utot 2576187
2556 Utot 2777572
2557 Utot 2707831
2558 Utot 2842877
2559 Utot 2754025
2560 Utot 2512592
2561 Utot 2699846
2562 Utot 2830229
2563 Utot 2827523
2564 Utot 2690075
2565 Utot 2609238
2566 Utot 2652456
2567 Utot 2734907
2568 Utot 2715079
2569 Utot 2848973
2570 Utot 2752515
2571 Utot 2710304
2572 Utot 2686731
2573 Utot 2648103
2574 Utot 2807122
2575 Utot 2749641
2576 Utot 2574155
2577 Utot 2780754
2578 Utot 2691606
2579 Utot 2930151
2580 Utot 2830032
2581 Utot 2788094
2582 Utot 2645985
2583 Utot 3096051
2584 Utot 2687896
2585 Utot 2712324
2586 Utot 2662745
2587 Utot 2560993
2588 Utot 2698302
2589 Utot 2647209
2590 Utot 2737804
2591 Utot 2817249
2592 Utot 2579154
2593 Utot 2736193
2594 Utot 2700872
2595 Utot 2580887
2596 Utot 2630470
2597 Utot 2830934
2598 Utot 2915103
2599 Utot 2932232
2600 Utot 2730206
2601 Utot 2709054
2602 Utot 2829837
2603 Utot 2927568
2604 Utot 2572941
2605 Utot 2690154
2606 Utot 2710020
2607 Utot 2713116
2608 Utot 2621638
2609 Utot 2945856
2610 Utot 2731114
2611 Utot 2675586
2612 Utot 2681476
2613 Utot 2610581
2614 Utot 2764469
2615 Utot 2714853
2616 Utot 2707127
2617 Utot 2701748
2618 Utot 2736266
2619 Utot 2552412
2620 Utot 2768724
2621 Utot 2652480
2622 Utot 2780499
2623 Utot 2899674
2624 Utot 2790229
2625 Utot 2507449
2626 Utot 2807633
2627 Utot 2619353
2628 Utot 2749412
2629 Utot 2628251
2630 Utot 2761743
2631 Utot 2635115
2632 Utot 2945521
2633 Utot 2798230
2634 Utot 2585796
2635 Utot 2448000
2636 Utot 2721496
2637 Utot 2766360
2638 Utot 2747817
2639 Utot 2605962
2640 Utot 2817938
2641 Utot 2577162
2642 Utot 2826988
2643 Utot 2663442
2644 Utot 2428243
2645 Utot 2824548
2646 Utot 2646663
2647 Utot 2763492
2648 Utot 2798860
2649 Utot 2751053
2650 Utot 2612195
2651 Utot 2724069
2652 Utot 2808416
2653 Utot 2732508
2654 Utot 2658123
2655 Utot 2718300
2656 Utot 2636128
2657 Utot 2644849
2658 Utot 2681276
2659 Utot 2818445
2660 Utot 2779362
2661 Utot 2699102
2662 Utot 2679214
2663 Utot 2802588
2664 Utot 2769134
2665 Utot 2682310
2666 Utot 3011742
2667 Utot 2678189
2668 Utot 2774770
2669 Utot 2782400
2670 Utot 2608312
2671 Utot 2717638
2672 Utot 2841990
2673 Utot 2886372
2674 Utot 2644015
2675 Utot 2549632
2676 Utot 2766218
2677 Utot 2750198
2678 Utot 2672989
2679 Utot 2761502
2680 Utot 2628897
2681 Utot 2664053
2682 Utot 2611645
2683 Utot 2589766
2684 Utot 2764507
2685 Utot 2698256
2686 Utot 2754679
2687 Utot 2667282
2688 Utot 2630867
2689 Utot 2875748
2690 Utot 2820728
2691 Utot 2710840
2692 Utot 2572802
2693 Utot 2695641
2694 Utot 2711905
2695 Utot 2739882
2696 Utot 2632150
2697 Utot 2863368
2698 Utot 2595405
2699 Utot 2682004
2700 Utot 2664531
2701 Utot 2660053
2702 Utot 2626868
2703 Utot 2692696
2704 Utot 2627044
2705 Utot 2968514
2706 Utot 2680492
2707 Utot 2698975
2708 Utot 2922516
2709 Utot 2783548
2710 Utot 2801566
2711 Utot 2804730
2712 Utot 2743442
2713 Utot 2858555
2714 Utot 2731500
2715 Utot 2644524
2716 Utot 2600018
2717 Utot 2516123
2718 Utot 2610950
2719 Utot 2702523
2720 Utot 2679369
2721 Utot 2705718
2722 Utot 2720157
2723 Utot 2692907
2724 Utot 2615475
2725 Utot 2719799
2726 Utot 2664966
2727 Utot 2832434
2728 Utot 2738777
2729 Utot 2876298
2730 Utot 2683514
2731 Utot 2733699
2732 Utot 2796591
2733 Utot 2737230
2734 Utot 2617061
2735 Utot 2699730
2736 Utot 2607766
2737 Utot 2813697
2738 Utot 2630410
2739 Utot 2701398
2740 Utot 2838653
2741 Utot 2721339
2742 Utot 2651987
2743 Utot 2650940
2744 Utot 2762216
2745 Utot 2651682
2746 Utot 2644911
2747 Utot 2615048
2748 Utot 2896962
2749 Utot 2614662
2750 Utot 2717394
2751 Utot 2786628
2752 Utot 2764300
2753 Utot 2597568
2754 Utot 2712244
2755 Utot 2394822
2756 Utot 2515389
2757 Utot 2722333
2758 Utot 2616312
2759 Utot 2784470
2760 Utot 2693789
2761 Utot 2797085
2762 Utot 2869965
2763 Utot 2956841
2764 Utot 2661196
2765 Utot 2821203
2766 Utot 2681809
2767 Utot 2586266
2768 Utot 2747297
2769 Utot 2798071
2770 Utot 2741234
2771 Utot 2650804
2772 Utot 2667804
2773 Utot 2777259
2774 Utot 2749152
2775 Utot 2653005
2776 Utot 2604081
2777 Utot 2614645
2778 Utot 2663692
2779 Utot 2809135
2780 Utot 2859786
2781 Utot 2731008
2782 Utot 2699118
2783 Utot 2631612
2784 Utot 2660085
2785 Utot 2638924
2786 Utot 2795686
2787 Utot 2709965
2788 Utot 2869809
2789 Utot 2733016
2790 Utot 2755204
2791 Utot 2894313
2792 Utot 2846518
2793 Utot 2621510
2794 Utot 2752302
2795 Utot 2810516
2796 Utot 2825499
2797 Utot 2923880
2798 Utot 2727782
2799 Utot 2716708
2800 Utot 2745573
2801 Utot 2696126
2802 Utot 2740982
2803 Utot 2555606
2804 Utot 2604109
2805 Utot 2670821
2806 Utot 2724977
2807 Utot 2857287
2808 Utot 2590389
2809 Utot 2794412
2810 Utot 2602079
2811 Utot 2508210
2812 Utot 2773178
2813 Utot 2553302
2814 Utot 2610640
2815 Utot 2754148
2816 Utot 2643599
2817 Utot 2657427
2818 Utot 2787599
2819 Utot 2858795
2820 Utot 2597518
2821 Utot 2460321
2822 Utot 2687053
2823 Utot 2844183
2824 Utot 2572194
2825 Utot 2597350
2826 Utot 2712802
2827 Utot 2782765
2828 Utot 2622689
2829 Utot 2829836
2830 Utot 2584626
2831 Utot 2719006
2832 Utot 2733052
2833 Utot 2552368
2834 Utot 2842510
2835 Utot 2586651
2836 Utot 2815583
2837 Utot 2745339
2838 Utot 2616628
2839 Utot 2735052
2840 Utot 2621168
2841 Utot 2650218
2842 Utot 2692022
2843 Utot 2760314
2844 Utot 2783801
2845 Utot 2577660
2846 Utot 2785914
2847 Utot 2523687
2848 Utot 2801738
2849 Utot 2685105
2850 Utot 2896043
2851 Utot 2982811
2852 Utot 2593275
2853 Utot 2610159
2854 Utot 2964016
2855 Utot 2806650
2856 Utot 2845913
2857 Utot 2657374
2858 Utot 2684051
2859 Utot 2656638
2860 Utot 2599302
2861 Utot 2714120
2862 Utot 2569071
2863 Utot 2969230
2864 Utot 2677156
2865 Utot 2669042
2866 Utot 2742956
2867 Utot 2565800
2868 Utot 2578241
2869 Utot 2703569
2870 Utot 2734995
2871 Utot 2733780
2872 Utot 2885243
2873 Utot 2779641
2874 Utot 2754601
2875 Utot 2901418
2876 Utot 2875602
2877 Utot 2590917
2878 Utot 2711035
2879 Utot 2725841
2880 Utot 2547118
2881 Utot 2743278
2882 Utot 2769362
2883 Utot 2547225
2884 Utot 2743237
2885 Utot 2729053
2886 Utot 2599452
2887 Utot 2662723
2888 Utot 2692061
2889 Utot 2767304
2890 Utot 2853381
2891 Utot 2635098
2892 Utot 2659529
2893 Utot 2457089
2894 Utot 2646849
2895 Utot 2612190
2896 Utot 2684506
2897 Utot 2848012
2898 Utot 2719164
2899 Utot 2656923
2900 Utot 2641076
2901 Utot 2893863
2902 Utot 2608787
2903 Utot 2873110
2904 Utot 2938445
2905 Utot 2841701
2906 Utot 2663358
2907 Utot 2849233
2908 Utot 2727558
2909 Utot 2519531
2910 Utot 2749239
2911 Utot 2744162
2912 Utot 2860706
2913 Utot 2706546
2914 Utot 2678381
2915 Utot 2895181
2916 Utot 2783861
2917 Utot 2652765
2918 Utot 2788885
2919 Utot 2581403
2920 Utot 2707447
2921 Utot 2787826
2922 Utot 2873174
2923 Utot 2687988
2924 Utot 2769713
2925 Utot 2760637
2926 Utot 2841267
2927 Utot 2768867
2928 Utot 2705415
2929 Utot 2646496
2930 Utot 2758122
2931 Utot 2687333
2932 Utot 2705706
2933 Utot 2872405
2934 Utot 2805774
2935 Utot 2641874
2936 Utot 2731806
2937 Utot 2721801
2938 Utot 2815122
2939 Utot 2799708
2940 Utot 2590898
2941 Utot 2801096
2942 Utot 2800610
2943 Utot 2679589
2944 Utot 2788510
2945 Utot 2851151
2946 Utot 2657355
2947 Utot 2483495
2948 Utot 2704468
2949 Utot 2553151
2950 Utot 2550685
2951 Utot 2723282
2952 Utot 2740933
2953 Utot 2865062
2954 Utot 2748334
2955 Utot 2680067
2956 Utot 2768071
2957 Utot 2653621
2958 Utot 2632921
2959 Utot 2750088
2960 Utot 2815414
2961 Utot 2803926
2962 Utot 2719036
2963 Utot 2912713
2964 Utot 2718632
2965 Utot 2839846
2966 Utot 2773046
2967 Utot 2813581
2968 Utot 2697711
2969 Utot 2742761
2970 Utot 2790785
2971 Utot 2553992
2972 Utot 2930881
2973 Utot 2687085
2974 Utot 2861549
2975 Utot 2786011
2976 Utot 2954538
2977 Utot 2889810
2978 Utot 2640973
2979 Utot 2645288
2980 Utot 2686641
2981 Utot 2628777
2982 Utot 2683785
2983 Utot 2730237
2984 Utot 2591527
2985 Utot 2743887
2986 Utot 2662150
2987 Utot 2840066
2988 Utot 2781882
2989 Utot 2761507
2990 Utot 2746119
2991 Utot 2746787
2992 Utot 2681817
2993 Utot 2633672
2994 Utot 2819073
2995 Utot 2658141
2996 Utot 2807684
2997 Utot 2692705
2998 Utot 2821619
2999 Utot 2685566
3000 Utot 2735932
3001 Utot 2746325
3002 Utot 2740822
3003 Utot 2733416
3004 Utot 2531167
3005 Utot 2790488
3006 Utot 2858706
3007 Utot 2706798
3008 Utot 2703827
3009 Utot 2468342
3010 Utot 2918679
3011 Utot 2581338
3012 Utot 2814906
3013 Utot 2772076
3014 Utot 2749885
3015 Utot 2727011
3016 Utot 2899860
3017 Utot 2890977
3018 Utot 2787309
3019 Utot 2822968
3020 Utot 2756690
3021 Utot 2790895
3022 Utot 2905348
3023 Utot 2536556
3024 Utot 2787684
3025 Utot 2815189
3026 Utot 2677964
3027 Utot 2864106
3028 Utot 2618930
3029 Utot 2619374
3030 Utot 2725622
3031 Utot 2748003
3032 Utot 2650582
3033 Utot 2683559
3034 Utot 2637835
3035 Utot 2869169
3036 Utot 2749762
3037 Utot 2723863
3038 Utot 2664365
3039 Utot 2676252
3040 Utot 2755525
3041 Utot 2683537
3042 Utot 2841310
3043 Utot 2730750
3044 Utot 2859533
3045 Utot 2696491
3046 Utot 2764454
3047 Utot 2853433
3048 Utot 2691995
3049 Utot 2824152
3050 Utot 2709791
3051 Utot 2792498
3052 Utot 2669218
3053 Utot 2481563
3054 Utot 2815633
3055 Utot 2501784
3056 Utot 2845944
3057 Utot 2895173
3058 Utot 2706572
3059 Utot 2754715
3060 Utot 2728876
3061 Utot 2902632
3062 Utot 2833397
3063 Utot 2688646
3064 Utot 2666319
3065 Utot 2640942
3066 Utot 2582198
3067 Utot 2611344
3068 Utot 2753129
3069 Utot 2675645
3070 Utot 2871560
3071 Utot 2733478
3072 Utot 2614616
3073 Utot 2712443
3074 Utot 2570859
3075 Utot 2673838
3076 Utot 2723699
3077 Utot 2793679
3078 Utot 2805167
3079 Utot 2618303
3080 Utot 2805571
3081 Utot 2734214
3082 Utot 2716021
3083 Utot 2681652
3084 Utot 2631418
3085 Utot 2747996
3086 Utot 2618165
3087 Utot 2659287
3088 Utot 2811579
3089 Utot 2667203
3090 Utot 2611909
3091 Utot 2796743
3092 Utot 2778768
3093 Utot 2612666
3094 Utot 2720456
3095 Utot 2683354
3096 Utot 2756927
3097 Utot 2898093
3098 Utot 2702365
3099 Utot 2724569
3100 Utot 2749290
3101 Utot 2676514
3102 Utot 2729535
3103 Utot 2535387
3104 Utot 2727886
3105 Utot 2656324
3106 Utot 2893675
3107 Utot 2618974
3108 Utot 2770719
3109 Utot 2663226
3110 Utot 2820515
3111 Utot 2711795
3112 Utot 2637186
3113 Utot 2567548
3114 Utot 2679409
3115 Utot 2486999
3116 Utot 2715584
3117 Utot 2605169
3118 Utot 2589778
3119 Utot 2575277
3120 Utot 2645661
3121 Utot 2678330
3122 Utot 2883877
3123 Utot 2835624
3124 Utot 2630882
3125 Utot 2920653
3126 Utot 2612435
3127 Utot 2849253
3128 Utot 2541093
3129 Utot 2729563
3130 Utot 2560177
3131 Utot 2607731
3132 Utot 2691780
3133 Utot 2829194
3134 Utot 2678277
3135 Utot 2552832
3136 Utot 2811361
3137 Utot 2618736
3138 Utot 2767175
3139 Utot 2645629
3140 Utot 2762385
3141 Utot 2636250
3142 Utot 2743631
3143 Utot 2733498
3144 Utot 2695826
3145 Utot 2778933
3146 Utot 2691389
3147 Utot 2682479
3148 Utot 2743752
3149 Utot 2800666
3150 Utot 2794168
3151 Utot 2638189
3152 Utot 2641935
3153 Utot 2814411
3154 Utot 2569077
3155 Utot 2748827
3156 Utot 2796505
3157 Utot 2781311
3158 Utot 2712254
3159 Utot 2867769
3160 Utot 2727194
3161 Utot 2714166
3162 Utot 2643857
3163 Utot 2749619
3164 Utot 2882082
3165 Utot 2653437
3166 Utot 2663325
3167 Utot 2772397
3168 Utot 2957520
3169 Utot 2710200
3170 Utot 2671152
3171 Utot 2709594
3172 Utot 2710728
3173 Utot 2683311
3174 Utot 2764900
3175 Utot 2448238
3176 Utot 2760756
3177 Utot 2715216
3178 Utot 2570083
3179 Utot 2841201
3180 Utot 2680108
3181 Utot 2918481
3182 Utot 2749121
3183 Utot 2644281
3184 Utot 2852000
3185 Utot 2774000
3186 Utot 2679408
3187 Utot 2812947
3188 Utot 2697998
3189 Utot 2567913
3190 Utot 2843748
3191 Utot 2617192
3192 Utot 2568638
3193 Utot 2729225
3194 Utot 2706225
3195 Utot 2596708
3196 Utot 2637739
3197 Utot 2664835
3198 Utot 2691484
3199 Utot 2722051
3200 Utot 2784646
3201 Utot 2843596
3202 Utot 2750732
3203 Utot 2579625
3204 Utot 2611665
3205 Utot 2798487
3206 Utot 2724803
3207 Utot 2684917
3208 Utot 2574637
3209 Utot 2928169
3210 Utot 2571891
3211 Utot 2761950
3212 Utot 2956717
3213 Utot 2708360
3214 Utot 2974869
3215 Utot 2599392
3216 Utot 2547404
3217 Utot 2745703
3218 Utot 2802572
3219 Utot 2623249
3220 Utot 2746460
3221 Utot 2747057
3222 Utot 2903756
3223 Utot 2670492
3224 Utot 2808927
3225 Utot 2653836
3226 Utot 2844719
3227 Utot 2781058
3228 Utot 2560247
3229 Utot 2723070
3230 Utot 2740845
3231 Utot 2726392
3232 Utot 2838885
3233 Utot 2579648
3234 Utot 2529369
3235 Utot 2644978
3236 Utot 2706568
3237 Utot 2760322
3238 Utot 2663057
3239 Utot 2579436
3240 Utot 2634961
3241 Utot 3013917
3242 Utot 2709001
3243 Utot 2687106
3244 Utot 2703923
3245 Utot 2616003
3246 Utot 2730714
3247 Utot 2734292
3248 Utot 2726206
3249 Utot 2678949
3250 Utot 2826693
3251 Utot 2614040
3252 Utot 2642656
3253 Utot 2601291
3254 Utot 2795239
3255 Utot 2672921
3256 Utot 2746533
3257 Utot 2745180
3258 Utot 2747929
3259 Utot 2775328
3260 Utot 2840869
3261 Utot 2685592
3262 Utot 2645980
3263 Utot 2535063
3264 Utot 2771847
3265 Utot 2783850
3266 Utot 2679823
3267 Utot 2646074
3268 Utot 2803459
3269 Utot 2595381
3270 Utot 2748928
3271 Utot 2823625
3272 Utot 2898523
3273 Utot 3029687
3274 Utot 2773874
3275 Utot 2727224
3276 Utot 2734865
3277 Utot 2818077
3278 Utot 2762628
3279 Utot 2632905
3280 Utot 2797607
3281 Utot 2559308
3282 Utot 2563630
3283 Utot 2883845
3284 Utot 2852065
3285 Utot 2503738
3286 Utot 2728561
3287 Utot 2734351
3288 Utot 2859309
3289 Utot 2734176
3290 Utot 2552785
3291 Utot 2650273
3292 Utot 2649217
3293 Utot 2753166
3294 Utot 2700736
3295 Utot 2711575
3296 Utot 2748198
3297 Utot 2693566
3298 Utot 2769473
3299 Utot 2595343
3300 Utot 2581938
3301 Utot 2768064
3302 Utot 2611755
3303 Utot 2496737
3304 Utot 2605214
3305 Utot 2680529
3306 Utot 2782329
3307 Utot 2909167
3308 Utot 2562865
3309 Utot 2918814
3310 Utot 2730696
3311 Utot 3074014
3312 Utot 2636853
3313 Utot 2838147
3314 Utot 2598530
3315 Utot 2735084
3316 Utot 2454812
3317 Utot 2648922
3318 Utot 2577377
3319 Utot 2666227
3320 Utot 2803661
3321 Utot 2773039
3322 Utot 2870641
3323 Utot 2603810
3324 Utot 2762430
3325 Utot 2652160
3326 Utot 2599261
3327 Utot 2519821
3328 Utot 2719705
3329 Utot 2645922
3330 Utot 2729319
3331 Utot 2713263
3332 Utot 2791334
3333 Utot 2712444
3334 Utot 2766852
3335 Utot 2613631
3336 Utot 2596063
3337 Utot 2660579
3338 Utot 2787155
3339 Utot 2650982
3340 Utot 2671984
3341 Utot 2659147
3342 Utot 2550500
3343 Utot 2672866
3344 Utot 2589414
3345 Utot 2734106
3346 Utot 2609759
3347 Utot 2576227
3348 Utot 2859945
3349 Utot 2780620
3350 Utot 2893274
3351 Utot 2554782
3352 Utot 2827353
3353 Utot 2770437
3354 Utot 2562350
3355 Utot 2798051
3356 Utot 2800162
3357 Utot 2660401
3358 Utot 2769410
3359 Utot 2830389
3360 Utot 2891782
3361 Utot 2792942
3362 Utot 2632520
3363 Utot 2734529
3364 Utot 2802269
3365 Utot 2661187
3366 Utot 2535155
3367 Utot 2664198
3368 Utot 2711589
3369 Utot 2685195
3370 Utot 2789444
3371 Utot 2583074
3372 Utot 2647040
3373 Utot 2851269
3374 Utot 2704929
3375 Utot 2758286
3376 Utot 2727875
3377 Utot 2656128
3378 Utot 2675579
3379 Utot 2690179
3380 Utot 2608122
3381 Utot 2574141
3382 Utot 2569043
3383 Utot 2640780
3384 Utot 2658874
3385 Utot 2687802
3386 Utot 2871389
3387 Utot 2582433
3388 Utot 2689726
3389 Utot 2627489
3390 Utot 2699148
3391 Utot 2847554
3392 Utot 2583111
3393 Utot 2716563
3394 Utot 2794584
3395 Utot 2629455
3396 Utot 2722197
3397 Utot 2681719
3398 Utot 2566169
3399 Utot 2762546
3400 Utot 2694113
3401 Utot 2774003
3402 Utot 2608083
3403 Utot 2714489
3404 Utot 2871973
3405 Utot 2798553
3406 Utot 2757534
3407 Utot 2798637
3408 Utot 2765725
3409 Utot 2522749
3410 Utot 2694330
3411 Utot 2690594
3412 Utot 2645348
3413 Utot 2727054
3414 Utot 2758074
3415 Utot 2745063
3416 Utot 2746636
3417 Utot 2856461
3418 Utot 2684350
3419 Utot 2560002
3420 Utot 2619008
3421 Utot 2637049
3422 Utot 2833207
3423 Utot 2774882
3424 Utot 2980105
3425 Utot 2897293
3426 Utot 2629372
3427 Utot 2592530
3428 Utot 2693271
3429 Utot 2508924
3430 Utot 2648043
3431 Utot 2906156
3432 Utot 2591477
3433 Utot 2519544
3434 Utot 2870429
3435 Utot 2825686
3436 Utot 2753483
3437 Utot 2517856
3438 Utot 2748610
3439 Utot 2639650
3440 Utot 2781677
3441 Utot 2702265
3442 Utot 2680730
3443 Utot 2580857
3444 Utot 2561568
3445 Utot 2795381
3446 Utot 2627217
3447 Utot 2652016
3448 Utot 2563328
3449 Utot 2754500
3450 Utot 2842736
3451 Utot 2866005
3452 Utot 2761392
3453 Utot 2662856
3454 Utot 2818088
3455 Utot 2594907
3456 Utot 2883328
3457 Utot 2716775
3458 Utot 2697577
3459 Utot 2689067
3460 Utot 2673328
3461 Utot 2668918
3462 Utot 2722666
3463 Utot 2711179
3464 Utot 2621000
3465 Utot 2669950
3466 Utot 2638697
3467 Utot 2713771
3468 Utot 2697229
3469 Utot 2758472
3470 Utot 2903225
3471 Utot 2660320
3472 Utot 2703437
3473 Utot 2595270
3474 Utot 2558686
3475 Utot 2779014
3476 Utot 2826439
3477 Utot 2537512
3478 Utot 2602842
3479 Utot 2705165
3480 Utot 2528797
3481 Utot 2804126
3482 Utot 2857781
3483 Utot 2756156
3484 Utot 2788715
3485 Utot 2657847
3486 Utot 2742490
3487 Utot 2741672
3488 Utot 2629992
3489 Utot 2745165
3490 Utot 2674684
3491 Utot 3024558
3492 Utot 2822362
3493 Utot 2815161
3494 Utot 2664001
3495 Utot 2661271
3496 Utot 2723889
3497 Utot 2522107
3498 Utot 2935821
3499 Utot 2719761
3500 Utot 2861760
3501 Utot 2793897
3502 Utot 2844261
3503 Utot 2650811
3504 Utot 2653463
3505 Utot 2728434
3506 Utot 2745208
3507 Utot 2660599
3508 Utot 2768965
3509 Utot 2662025
3510 Utot 2795574
3511 Utot 2729579
3512 Utot 2751717
3513 Utot 2664084
3514 Utot 2687019
3515 Utot 2885015
3516 Utot 2646594
3517 Utot 2687394
3518 Utot 2491994
3519 Utot 2714473
3520 Utot 2685186
3521 Utot 2728812
3522 Utot 2600076
3523 Utot 2651640
3524 Utot 2687203
3525 Utot 2558586
3526 Utot 2680884
3527 Utot 2668967
3528 Utot 2618662
3529 Utot 2765641
3530 Utot 2707468
3531 Utot 2656272
3532 Utot 2658685
3533 Utot 2808869
3534 Utot 2722614
3535 Utot 2625964
3536 Utot 2710792
3537 Utot 2646567
3538 Utot 2832407
3539 Utot 2740231
3540 Utot 2719199
3541 Utot 2833520
3542 Utot 2575965
3543 Utot 2690728
3544 Utot 2574625
3545 Utot 2804026
3546 Utot 2843524
3547 Utot 2564670
3548 Utot 2879340
3549 Utot 2680683
3550 Utot 2675638
3551 Utot 2972124
3552 Utot 2715324
3553 Utot 2718451
3554 Utot 2687537
3555 Utot 2824345
3556 Utot 2658592
3557 Utot 2833847
3558 Utot 2692415
3559 Utot 2694078
3560 Utot 2509261
3561 Utot 2844971
3562 Utot 2985524
3563 Utot 2734523
3564 Utot 2568009
3565 Utot 2703651
3566 Utot 2736591
3567 Utot 2728049
3568 Utot 2564850
3569 Utot 2804949
3570 Utot 2666287
3571 Utot 2610776
3572 Utot 2765853
3573 Utot 2698928
3574 Utot 2669502
3575 Utot 2742229
3576 Utot 2657974
3577 Utot 2574381
3578 Utot 2861913
3579 Utot 2657729
3580 Utot 2749740
3581 Utot 2654356
3582 Utot 2850983
3583 Utot 2560086
3584 Utot 2885416
3585 Utot 2718142
3586 Utot 2577808
3587 Utot 2713786
3588 Utot 2670356
3589 Utot 2814699
3590 Utot 2792041
3591 Utot 2817743
3592 Utot 2745804
3593 Utot 2699853
3594 Utot 2686188
3595 Utot 2515356
3596 Utot 2591159
3597 Utot 2670475
3598 Utot 2784239
3599 Utot 2581617
3600 Utot 2685219
3601 Utot 2705796
3602 Utot 2714392
3603 Utot 2752790
3604 Utot 2621762
3605 Utot 2657676
3606 Utot 2681644
3607 Utot 2926236
3608 Utot 2777324
3609 Utot 2819542
3610 Utot 2672324
3611 Utot 2681155
3612 Utot 2952723
3613 Utot 2753294
3614 Utot 2747255
3615 Utot 2868510
3616 Utot 2539338
3617 Utot 2697930
3618 Utot 2688269
3619 Utot 2556621
3620 Utot 2724666
3621 Utot 2595298
3622 Utot 2790962
3623 Utot 2698642
3624 Utot 2885009
3625 Utot 2664581
3626 Utot 2810524
3627 Utot 2688647
3628 Utot 2589355
3629 Utot 2697823
3630 Utot 2931154
3631 Utot 2596380
3632 Utot 2743303
3633 Utot 2549874
3634 Utot 2598797
3635 Utot 2773082
3636 Utot 2655436
3637 Utot 2718947
3638 Utot 2573321
3639 Utot 2840013
3640 Utot 2716901
3641 Utot 2794913
3642 Utot 2464026
3643 Utot 2621654
3644 Utot 2863368
3645 Utot 2905623
3646 Utot 2729576
3647 Utot 2670959
3648 Utot 2770366
3649 Utot 2751725
3650 Utot 2638835
3651 Utot 2616592
3652 Utot 2733286
3653 Utot 2648630
3654 Utot 2785422
3655 Utot 2824497
3656 Utot 2652891
3657 Utot 2704147
3658 Utot 2580123
3659 Utot 2574434
3660 Utot 2691683
3661 Utot 2610805
3662 Utot 2742790
3663 Utot 2770470
3664 Utot 2565739
3665 Utot 2646353
3666 Utot 2792291
3667 Utot 2712908
3668 Utot 2679693
3669 Utot 2562469
3670 Utot 2707845
3671 Utot 2687178
3672 Utot 2532924
3673 Utot 2610535
3674 Utot 2640048
3675 Utot 2570698
3676 Utot 2667359
3677 Utot 2612430
3678 Utot 2662416
3679 Utot 2802605
3680 Utot 2716184
3681 Utot 2686894
3682 Utot 2850023
3683 Utot 2673437
3684 Utot 2797641
3685 Utot 2804619
3686 Utot 2693745
3687 Utot 2681100
3688 Utot 2694997
3689 Utot 2707515
3690 Utot 2538583
3691 Utot 2867910
3692 Utot 2659528
3693 Utot 2704768
3694 Utot 2773949
3695 Utot 2800872
3696 Utot 2460992
3697 Utot 2692843
3698 Utot 2739944
3699 Utot 2714533
3700 Utot 2641285
3701 Utot 2622031
3702 Utot 2811311
3703 Utot 2983024
3704 Utot 2679425
3705 Utot 2934651
3706 Utot 2898703
3707 Utot 2712583
3708 Utot 2681973
3709 Utot 2735186
3710 Utot 2717923
3711 Utot 2787279
3712 Utot 2841537
3713 Utot 2655694
3714 Utot 2957548
3715 Utot 2619120
3716 Utot 2786861
3717 Utot 2667654
3718 Utot 2514984
3719 Utot 2655761
3720 Utot 2762995
3721 Utot 2905679
3722 Utot 2780953
3723 Utot 2776398
3724 Utot 2786533
3725 Utot 2585720
3726 Utot 2610907
3727 Utot 2769260
3728 Utot 2790485
3729 Utot 2703742
3730 Utot 2774132
3731 Utot 2624839
3732 Utot 2946200
3733 Utot 2714026
3734 Utot 2821812
3735 Utot 2516140
3736 Utot 2864472
3737 Utot 2756918
3738 Utot 2614712
3739 Utot 2641690
3740 Utot 2604271
3741 Utot 2687839
3742 Utot 2687669
3743 Utot 2606426
3744 Utot 2556790
3745 Utot 2672603
3746 Utot 2639592
3747 Utot 2913240
3748 Utot 2523182
3749 Utot 2638732
3750 Utot 2577304
3751 Utot 2750776
3752 Utot 2710152
3753 Utot 2743881
3754 Utot 2586857
3755 Utot 2685205
3756 Utot 2712875
3757 Utot 2716011
3758 Utot 2716648
3759 Utot 2709002
3760 Utot 2747864
3761 Utot 2481524
3762 Utot 2753844
3763 Utot 2630427
3764 Utot 2568117
3765 Utot 2714825
3766 Utot 2778888
3767 Utot 2538625
3768 Utot 2874860
3769 Utot 2702445
3770 Utot 2711289
3771 Utot 2637297
3772 Utot 2926879
3773 Utot 2687236
3774 Utot 2681277
3775 Utot 2929240
3776 Utot 2683371
3777 Utot 2719200
3778 Utot 2758654
3779 Utot 2723955
3780 Utot 2605435
3781 Utot 2646852
3782 Utot 2611821
3783 Utot 2619661
3784 Utot 2748776
3785 Utot 2816123
3786 Utot 2781350
3787 Utot 2771920
3788 Utot 2623450
3789 Utot 2616670
3790 Utot 2817148
3791 Utot 2756076
3792 Utot 2780033
3793 Utot 2588621
3794 Utot 2686620
3795 Utot 2721602
3796 Utot 2706384
3797 Utot 2721314
3798 Utot 2828731
3799 Utot 2659431
3800 Utot 2708327
3801 Utot 2668482
3802 Utot 2678707
3803 Utot 2584633
3804 Utot 3005231
3805 Utot 2644194
3806 Utot 2672674
3807 Utot 2721638
3808 Utot 2805305
3809 Utot 2892118
3810 Utot 2654994
3811 Utot 2734668
3812 Utot 2674601
3813 Utot 2763881
3814 Utot 2599829
3815 Utot 2578334
3816 Utot 2529336
3817 Utot 2690313
3818 Utot 2749187
3819 Utot 2653187
3820 Utot 2561580
3821 Utot 2729427
3822 Utot 2818355
3823 Utot 2793147
3824 Utot 2618666
3825 Utot 2746918
3826 Utot 2723405
3827 Utot 2529261
3828 Utot 2819002
3829 Utot 2721147
3830 Utot 2594118
3831 Utot 2739792
3832 Utot 2840551
3833 Utot 2810780
3834 Utot 2699813
3835 Utot 2741648
3836 Utot 2879651
3837 Utot 2721537
3838 Utot 2778123
3839 Utot 2754787
3840 Utot 2593171
3841 Utot 2623078
3842 Utot 2646432
3843 Utot 2763805
3844 Utot 2710820
3845 Utot 2695580
3846 Utot 2819179
3847 Utot 2651254
3848 Utot 2876605
3849 Utot 2572575
3850 Utot 2751333
3851 Utot 2580913
3852 Utot 2657689
3853 Utot 2662872
3854 Utot 2727596
3855 Utot 2878858
3856 Utot 2800577
3857 Utot 2860738
3858 Utot 2675010
3859 Utot 2627258
3860 Utot 2632325
3861 Utot 2632859
3862 Utot 2591805
3863 Utot 3007042
3864 Utot 2751924
3865 Utot 2593610
3866 Utot 2809678
3867 Utot 2643269
3868 Utot 2763653
3869 Utot 2719812
3870 Utot 2746372
3871 Utot 2699876
3872 Utot 2757870
3873 Utot 2745932
3874 Utot 2754746
3875 Utot 2785609
3876 Utot 2640312
3877 Utot 2732304
3878 Utot 2661937
3879 Utot 2542490
3880 Utot 2661902
3881 Utot 2661860
3882 Utot 2581329
3883 Utot 2741929
3884 Utot 2570898
3885 Utot 2579573
3886 Utot 2944383
3887 Utot 2796659
3888 Utot 2788765
3889 Utot 2618938
3890 Utot 2626571
3891 Utot 2559972
3892 Utot 2626742
3893 Utot 2750509
3894 Utot 2809646
3895 Utot 2931939
3896 Utot 2702406
3897 Utot 2629968
3898 Utot 2612693
3899 Utot 2670492
3900 Utot 2589128
3901 Utot 2652454
3902 Utot 2746687
3903 Utot 2516620
3904 Utot 2509805
3905 Utot 2772317
3906 Utot 2771110
3907 Utot 2623542
3908 Utot 2664750
3909 Utot 2837487
3910 Utot 2798337
3911 Utot 2754753
3912 Utot 2680695
3913 Utot 2740246
3914 Utot 2659028
3915 Utot 2716198
3916 Utot 2866740
3917 Utot 2767648
3918 Utot 2994117
3919 Utot 2734737
3920 Utot 2725405
3921 Utot 2637113
3922 Utot 2631906
3923 Utot 2647752
3924 Utot 2685440
3925 Utot 2820395
3926 Utot 2632496
3927 Utot 2897366
3928 Utot 2747188
3929 Utot 2789892
3930 Utot 2831883
3931 Utot 2540058
3932 Utot 2789655
3933 Utot 2715182
3934 Utot 2667775
3935 Utot 2754004
3936 Utot 2833461
3937 Utot 2875152
3938 Utot 2768416
3939 Utot 2626842
3940 Utot 2738667
3941 Utot 2720235
3942 Utot 2669507
3943 Utot 2574234
3944 Utot 2625225
3945 Utot 2769059
3946 Utot 2576873
3947 Utot 2745430
3948 Utot 2965732
3949 Utot 2634203
3950 Utot 2838141
3951 Utot 2804159
3952 Utot 2785506
3953 Utot 2897542
3954 Utot 2750490
3955 Utot 2772239
3956 Utot 2746792
3957 Utot 2764776
3958 Utot 2703023
3959 Utot 2518342
3960 Utot 2883507
3961 Utot 2630726
3962 Utot 2877413
3963 Utot 2744835
3964 Utot 2802642
3965 Utot 2630052
3966 Utot 2743319
3967 Utot 2670463
3968 Utot 2879161
3969 Utot 2590677
3970 Utot 2639307
3971 Utot 2788224
3972 Utot 2794000
3973 Utot 2704849
3974 Utot 2623970
3975 Utot 2695663
3976 Utot 2920341
3977 Utot 2630806
3978 Utot 2458344
3979 Utot 2698603
3980 Utot 2706065
3981 Utot 2736629
3982 Utot 2677345
3983 Utot 2708087
3984 Utot 2811897
3985 Utot 2653362
3986 Utot 2858453
3987 Utot 2654476
3988 Utot 2694729
3989 Utot 2593536
3990 Utot 2658914
3991 Utot 2575731
3992 Utot 2623955
3993 Utot 2663471
3994 Utot 2838967
3995 Utot 2648586
3996 Utot 2782953
3997 Utot 2647932
3998 Utot 2591944
3999 Utot 2781419
4000 Utot 2811001
4001 Utot 2741028
4002 Utot 2893322
4003 Utot 2736575
4004 Utot 2716916
4005 Utot 2561813
4006 Utot 2711812
4007 Utot 2777610
4008 Utot 2493939
4009 Utot 2712732
4010 Utot 2772044
4011 Utot 2797473
4012 Utot 2732737
4013 Utot 2811992
4014 Utot 2695016
4015 Utot 2743701
4016 Utot 2611606
4017 Utot 2816098
4018 Utot 2650335
4019 Utot 2749333
4020 Utot 3010652
4021 Utot 2565416
4022 Utot 2817646
4023 Utot 2507207
4024 Utot 2542766
4025 Utot 2923604
4026 Utot 2754943
4027 Utot 2682966
4028 Utot 2659029
4029 Utot 2762314
4030 Utot 2721115
4031 Utot 2850100
4032 Utot 2689256
4033 Utot 2746526
4034 Utot 2612776
4035 Utot 2444836
4036 Utot 2662762
4037 Utot 2641174
4038 Utot 2802887
4039 Utot 2679641
4040 Utot 2679864
4041 Utot 2842520
4042 Utot 2803700
4043 Utot 2543157
4044 Utot 2746670
4045 Utot 2695776
4046 Utot 2767922
4047 Utot 2643677
4048 Utot 2749348
4049 Utot 2749950
4050 Utot 2756025
4051 Utot 2581567
4052 Utot 2749720
4053 Utot 2687319
4054 Utot 2666861
4055 Utot 2738183
4056 Utot 2702225
4057 Utot 2637285
4058 Utot 2777172
4059 Utot 2641786
4060 Utot 2801116
4061 Utot 2712741
4062 Utot 2617697
4063 Utot 2451816
4064 Utot 2810807
4065 Utot 2698664
4066 Utot 2749770
4067 Utot 2954199
4068 Utot 2652058
4069 Utot 2652334
4070 Utot 2788357
4071 Utot 2815958
4072 Utot 2599901
4073 Utot 2646509
4074 Utot 2601057
4075 Utot 2939711
4076 Utot 2648724
4077 Utot 2810867
4078 Utot 2772574
4079 Utot 2773357
4080 Utot 2612342
4081 Utot 2722701
4082 Utot 2722755
4083 Utot 2839408
4084 Utot 2736709
4085 Utot 2636908
4086 Utot 2806499
4087 Utot 2584179
4088 Utot 2776549
4089 Utot 2720490
4090 Utot 2760046
4091 Utot 2812517
4092 Utot 2826609
4093 Utot 2822984
4094 Utot 2591521
4095 Utot 2566930
4096 Utot 2762678
4097 Utot 2631161
4098 Utot 2622654
4099 Utot 2591430
4100 Utot 2666929
4101 Utot 2746391
4102 Utot 2710928
4103 Utot 2684068
4104 Utot 2644047
4105 Utot 2419792
4106 Utot 2694959
4107 Utot 2809336
4108 Utot 2793578
4109 Utot 2779465
4110 Utot 2750530
4111 Utot 2991762
4112 Utot 2697213
4113 Utot 2730758
4114 Utot 2423462
4115 Utot 2612781
4116 Utot 2831488
4117 Utot 2579166
4118 Utot 2797761
4119 Utot 2788431
4120 Utot 2946709
4121 Utot 2769367
4122 Utot 2692824
4123 Utot 2610389
4124 Utot 2601489
4125 Utot 2671039
4126 Utot 2833971
4127 Utot 3031499
4128 Utot 2641847
4129 Utot 2724162
4130 Utot 2817529
4131 Utot 2704229
4132 Utot 2580075
4133 Utot 2778392
4134 Utot 2753012
4135 Utot 2784953
4136 Utot 2793292
4137 Utot 2702468
4138 Utot 2738162
4139 Utot 2715646
4140 Utot 2487752
4141 Utot 2684660
4142 Utot 2730819
4143 Utot 2584883
4144 Utot 2682260
4145 Utot 2703215
4146 Utot 2474606
4147 Utot 2774409
4148 Utot 2658929
4149 Utot 2599252
4150 Utot 2443754
4151 Utot 2694422
4152 Utot 2677742
4153 Utot 2649999
4154 Utot 2583655
4155 Utot 2792926
4156 Utot 2752898
4157 Utot 2799944
4158 Utot 2672335
4159 Utot 2978234
4160 Utot 2844256
4161 Utot 2704426
4162 Utot 2667598
4163 Utot 2653646
4164 Utot 2561872
4165 Utot 2665327
4166 Utot 2514080
4167 Utot 2721306
4168 Utot 2906557
4169 Utot 2607518
4170 Utot 2754210
4171 Utot 2808152
4172 Utot 2777134
4173 Utot 2730773
4174 Utot 2819852
4175 Utot 2583125
4176 Utot 2663066
4177 Utot 2671563
4178 Utot 2789529
4179 Utot 2826505
4180 Utot 2624220
4181 Utot 2781327
4182 Utot 2723138
4183 Utot 2554272
4184 Utot 2730696
4185 Utot 2667409
4186 Utot 2696887
4187 Utot 2766015
4188 Utot 2717435
4189 Utot 2749464
4190 Utot 2767288
4191 Utot 2656613
4192 Utot 2708495
4193 Utot 2646293
4194 Utot 2762839
4195 Utot 2603897
4196 Utot 2736841
4197 Utot 2681486
4198 Utot 2673688
4199 Utot 2785105
4200 Utot 2655605
4201 Utot 2519923
4202 Utot 2882913
4203 Utot 2476639
4204 Utot 2709088
4205 Utot 2567997
4206 Utot 2751401
4207 Utot 2651074
4208 Utot 2652394
4209 Utot 2563900
4210 Utot 2774235
4211 Utot 2576153
4212 Utot 2818669
4213 Utot 2621351
4214 Utot 2624345
4215 Utot 2549995
4216 Utot 2584691
4217 Utot 2833159
4218 Utot 2606320
4219 Utot 2810390
4220 Utot 2666585
4221 Utot 2713440
4222 Utot 2690090
4223 Utot 2694737
4224 Utot 2747932
4225 Utot 2803847
4226 Utot 2685388
4227 Utot 2713390
4228 Utot 2703337
4229 Utot 2776466
4230 Utot 2592909
4231 Utot 2754688
4232 Utot 2707771
4233 Utot 2763755
4234 Utot 2867755
4235 Utot 2690005
4236 Utot 2668556
4237 Utot 2703981
4238 Utot 2744913
4239 Utot 2539538
4240 Utot 2709233
4241 Utot 2824492
4242 Utot 2772966
4243 Utot 2557598
4244 Utot 2637602
4245 Utot 2843126
4246 Utot 2870534
4247 Utot 2747128
4248 Utot 2770294
4249 Utot 2779278
4250 Utot 2697633
4251 Utot 2706401
4252 Utot 2812775
4253 Utot 2721127
4254 Utot 2695697
4255 Utot 2754245
4256 Utot 2809531
4257 Utot 2695758
4258 Utot 2755016
4259 Utot 2681027
4260 Utot 2723224
4261 Utot 2651321
4262 Utot 2719822
4263 Utot 2661116
4264 Utot 2660919
4265 Utot 2538398
4266 Utot 2715300
4267 Utot 2646945
4268 Utot 2729089
4269 Utot 2755265
4270 Utot 2421144
4271 Utot 2670876
4272 Utot 2984868
4273 Utot 2754719
4274 Utot 3061306
4275 Utot 2774983
4276 Utot 2632797
4277 Utot 2820604
4278 Utot 2585950
4279 Utot 2615942
4280 Utot 2731869
4281 Utot 2697770
4282 Utot 2803817
4283 Utot 2888849
4284 Utot 2884739
4285 Utot 2593602
4286 Utot 2735343
4287 Utot 2745548
4288 Utot 2789216
4289 Utot 2840215
4290 Utot 2629396
4291 Utot 2797141
4292 Utot 2734943
4293 Utot 2644977
4294 Utot 2580593
4295 Utot 2792530
4296 Utot 2715074
4297 Utot 2691412
4298 Utot 2534253
4299 Utot 2617709
4300 Utot 2810200
4301 Utot 2890225
4302 Utot 2611430
4303 Utot 2742524
4304 Utot 2691748
4305 Utot 2617690
4306 Utot 2751044
4307 Utot 2649979
4308 Utot 2779077
4309 Utot 2704379
4310 Utot 2966401
4311 Utot 2733250
4312 Utot 2823421
4313 Utot 2797586
4314 Utot 2772268
4315 Utot 2638052
4316 Utot 2603466
4317 Utot 2623679
4318 Utot 2782283
4319 Utot 2701180
4320 Utot 2723726
4321 Utot 2753959
4322 Utot 2694054
4323 Utot 2600965
4324 Utot 2905091
4325 Utot 2685023
4326 Utot 2734247
4327 Utot 2807912
4328 Utot 2842878
4329 Utot 2928306
4330 Utot 2673861
4331 Utot 2738156
4332 Utot 2831379
4333 Utot 2714049
4334 Utot 2772243
4335 Utot 2690129
4336 Utot 2650273
4337 Utot 2608904
4338 Utot 2567016
4339 Utot 2857217
4340 Utot 2708466
4341 Utot 2795032
4342 Utot 2787212
4343 Utot 2762202
4344 Utot 2670093
4345 Utot 2635525
4346 Utot 2763653
4347 Utot 2792369
4348 Utot 2602495
4349 Utot 2661143
4350 Utot 2734376
4351 Utot 2590498
4352 Utot 2770343
4353 Utot 2746083
4354 Utot 2545835
4355 Utot 2625261
4356 Utot 2750683
4357 Utot 2719509
4358 Utot 2747435
4359 Utot 2856961
4360 Utot 2598334
4361 Utot 2600676
4362 Utot 2645720
4363 Utot 2831293
4364 Utot 2747212
4365 Utot 2597862
4366 Utot 2759310
4367 Utot 2620497
4368 Utot 2679729
4369 Utot 2645662
4370 Utot 2656419
4371 Utot 2589147
4372 Utot 2735480
4373 Utot 2844684
4374 Utot 2770937
4375 Utot 2743326
4376 Utot 2795631
4377 Utot 2665532
4378 Utot 2778380
4379 Utot 2631639
4380 Utot 2835472
4381 Utot 2862734
4382 Utot 2809433
4383 Utot 2819873
4384 Utot 2752381
4385 Utot 2860011
4386 Utot 2973671
4387 Utot 2712083
4388 Utot 2764391
4389 Utot 2652999
4390 Utot 2608606
4391 Utot 2641160
4392 Utot 2729447
4393 Utot 2543405
4394 Utot 2703997
4395 Utot 2763326
4396 Utot 2797583
4397 Utot 2758281
4398 Utot 2771003
4399 Utot 2692081
4400 Utot 2776343
4401 Utot 2792986
4402 Utot 2666316
4403 Utot 2643858
4404 Utot 2592436
4405 Utot 2774516
4406 Utot 2637740
4407 Utot 2654223
4408 Utot 2682110
4409 Utot 2560294
4410 Utot 2695801
4411 Utot 2728731
4412 Utot 2555916
4413 Utot 2609674
4414 Utot 2785037
4415 Utot 2582855
4416 Utot 2884710
4417 Utot 2720477
4418 Utot 2538617
4419 Utot 2550653
4420 Utot 2773766
4421 Utot 2708826
4422 Utot 2625644
4423 Utot 2504646
4424 Utot 2680987
4425 Utot 2345681
4426 Utot 2649871
4427 Utot 2752046
4428 Utot 2621295
4429 Utot 2610765
4430 Utot 2635398
4431 Utot 2718854
4432 Utot 2708791
4433 Utot 2707360
4434 Utot 2664080
4435 Utot 2686626
4436 Utot 2775178
4437 Utot 2708700
4438 Utot 2791352
4439 Utot 2884399
4440 Utot 2512537
4441 Utot 2697822
4442 Utot 2735376
4443 Utot 2591566
4444 Utot 2663009
4445 Utot 2668523
4446 Utot 2565491
4447 Utot 2935251
4448 Utot 2603261
4449 Utot 2587987
4450 Utot 2569461
4451 Utot 2603288
4452 Utot 2839057
4453 Utot 2830353
4454 Utot 2642956
4455 Utot 2649408
4456 Utot 2653187
4457 Utot 2773424
4458 Utot 2749870
4459 Utot 2792155
4460 Utot 2708147
4461 Utot 2601312
4462 Utot 2532881
4463 Utot 2857916
4464 Utot 2748427
4465 Utot 2548706
4466 Utot 2934147
4467 Utot 2737105
4468 Utot 2695684
4469 Utot 2872914
4470 Utot 2690658
4471 Utot 2884455
4472 Utot 2841880
4473 Utot 2646289
4474 Utot 2698878
4475 Utot 2674264
4476 Utot 2626076
4477 Utot 2820483
4478 Utot 2576064
4479 Utot 2840880
4480 Utot 2643438
4481 Utot 2660264
4482 Utot 2880729
4483 Utot 3009382
4484 Utot 2815830
4485 Utot 2828111
4486 Utot 2703845
4487 Utot 2720080
4488 Utot 2725358
4489 Utot 2909556
4490 Utot 2668366
4491 Utot 2619610
4492 Utot 2645735
4493 Utot 2569775
4494 Utot 2547404
4495 Utot 2697886
4496 Utot 2742378
4497 Utot 2769009
4498 Utot 2472219
4499 Utot 2792021
4500 Utot 2747682
4501 Utot 2648034
4502 Utot 2661090
4503 Utot 2871402
4504 Utot 2673347
4505 Utot 2671217
4506 Utot 2788865
4507 Utot 2720231
4508 Utot 2671843
4509 Utot 2737722
4510 Utot 2671539
4511 Utot 2693889
4512 Utot 2690434
4513 Utot 2583818
4514 Utot 2551096
4515 Utot 2699757
4516 Utot 2813678
4517 Utot 2836744
4518 Utot 2736904
4519 Utot 2657879
4520 Utot 2804596
4521 Utot 2736526
4522 Utot 2689014
4523 Utot 2974481
4524 Utot 2819371
4525 Utot 2622729
4526 Utot 2774938
4527 Utot 2703311
4528 Utot 2606072
4529 Utot 2734795
4530 Utot 2719278
4531 Utot 2777052
4532 Utot 2836879
4533 Utot 2693790
4534 Utot 2744249
4535 Utot 2735606
4536 Utot 2914782
4537 Utot 2588155
4538 Utot 2714598
4539 Utot 2863114
4540 Utot 2661355
4541 Utot 2593750
4542 Utot 2907745
4543 Utot 2726969
4544 Utot 2673000
4545 Utot 2665259
4546 Utot 2722260
4547 Utot 2644625
4548 Utot 2720716
4549 Utot 2752324
4550 Utot 2705350
4551 Utot 2721456
4552 Utot 2914295
4553 Utot 2723847
4554 Utot 2750578
4555 Utot 2803869
4556 Utot 2734256
4557 Utot 2621408
4558 Utot 2754285
4559 Utot 2869582
4560 Utot 2559298
4561 Utot 2662190
4562 Utot 2597820
4563 Utot 2635891
4564 Utot 2698338
4565 Utot 2864510
4566 Utot 2819323
4567 Utot 2674801
4568 Utot 2727368
4569 Utot 2766565
4570 Utot 2746466
4571 Utot 2669211
4572 Utot 2895777
4573 Utot 2524986
4574 Utot 2780946
4575 Utot 2534981
4576 Utot 2786139
4577 Utot 2696923
4578 Utot 2801760
4579 Utot 2708592
4580 Utot 2751103
4581 Utot 2619548
4582 Utot 2721589
4583 Utot 2499486
4584 Utot 2532648
4585 Utot 2747687
4586 Utot 2791997
4587 Utot 2727224
4588 Utot 2851725
4589 Utot 2629481
4590 Utot 2579661
4591 Utot 2762490
4592 Utot 2695079
4593 Utot 2792703
4594 Utot 2804245
4595 Utot 2778312
4596 Utot 2535983
4597 Utot 2924855
4598 Utot 2812227
4599 Utot 2738333
4600 Utot 2689342
4601 Utot 2665958
4602 Utot 2705600
4603 Utot 2695475
4604 Utot 2617969
4605 Utot 2795973
4606 Utot 2675347
4607 Utot 2652899
4608 Utot 2815193
4609 Utot 2740822
4610 Utot 2692277
4611 Utot 2653863
4612 Utot 2807634
4613 Utot 2679907
4614 Utot 2759049
4615 Utot 2640021
4616 Utot 2745529
4617 Utot 2685568
4618 Utot 2600747
4619 Utot 2883971
4620 Utot 2755667
4621 Utot 2740567
4622 Utot 2604841
4623 Utot 2593651
4624 Utot 2669536
4625 Utot 2530971
4626 Utot 2913227
4627 Utot 2733624
4628 Utot 2609410
4629 Utot 2544683
4630 Utot 2621922
4631 Utot 2809624
4632 Utot 2675435
4633 Utot 2675570
4634 Utot 2536041
4635 Utot 2681266
4636 Utot 2696655
4637 Utot 2718861
4638 Utot 2758393
4639 Utot 2801009
4640 Utot 2564230
4641 Utot 3030380
4642 Utot 2736422
4643 Utot 2802694
4644 Utot 2575816
4645 Utot 2769501
4646 Utot 2631187
4647 Utot 2757092
4648 Utot 2613080
4649 Utot 2527134
4650 Utot 2670055
4651 Utot 2595905
4652 Utot 2607640
4653 Utot 2840077
4654 Utot 2892176
4655 Utot 2764805
4656 Utot 2666556
4657 Utot 2821653
4658 Utot 2746566
4659 Utot 2730701
4660 Utot 2775366
4661 Utot 2832423
4662 Utot 2790203
4663 Utot 2767420
4664 Utot 2743091
4665 Utot 2656296
4666 Utot 2827562
4667 Utot 2749379
4668 Utot 2701764
4669 Utot 2516980
4670 Utot 3001073
4671 Utot 2687542
4672 Utot 2787056
4673 Utot 2607839
4674 Utot 2702036
4675 Utot 2636616
4676 Utot 2528263
4677 Utot 2661303
4678 Utot 2611529
4679 Utot 2627912
4680 Utot 2844224
4681 Utot 2585000
4682 Utot 2686448
4683 Utot 2706677
4684 Utot 2694255
4685 Utot 2782805
4686 Utot 2579421
4687 Utot 2658754
4688 Utot 2715906
4689 Utot 2667967
4690 Utot 2761517
4691 Utot 2692533
4692 Utot 2730956
4693 Utot 2491699
4694 Utot 2791405
4695 Utot 2716434
4696 Utot 2686605
4697 Utot 2762408
4698 Utot 2916344
4699 Utot 2493396
4700 Utot 2666074
4701 Utot 2607974
4702 Utot 2660550
4703 Utot 2536378
4704 Utot 2769810
4705 Utot 2729290
4706 Utot 2673932
4707 Utot 2518666
4708 Utot 2746193
4709 Utot 2628774
4710 Utot 2656567
4711 Utot 2754521
4712 Utot 2724109
4713 Utot 2811094
4714 Utot 2764112
4715 Utot 2660351
4716 Utot 2728928
4717 Utot 2542085
4718 Utot 2527458
4719 Utot 2724380
4720 Utot 2804934
4721 Utot 2925205
4722 Utot 2777964
4723 Utot 2548404
4724 Utot 2867130
4725 Utot 2850501
4726 Utot 2886920
4727 Utot 2619910
4728 Utot 2706155
4729 Utot 2661379
4730 Utot 2629449
4731 Utot 2731984
4732 Utot 2752771
4733 Utot 2485568
4734 Utot 2691770
4735 Utot 2583618
4736 Utot 2526370
4737 Utot 2589631
4738 Utot 2699403
4739 Utot 2701242
4740 Utot 2758186
4741 Utot 2695163
4742 Utot 2726210
4743 Utot 2710162
4744 Utot 2456184
4745 Utot 2715378
4746 Utot 2771699
4747 Utot 2773632
4748 Utot 2728429
4749 Utot 2734065
4750 Utot 2732570
4751 Utot 2628245
4752 Utot 2737860
4753 Utot 2695277
4754 Utot 2556757
4755 Utot 2778698
4756 Utot 2831627
4757 Utot 2776479
4758 Utot 2801668
4759 Utot 2783479
4760 Utot 2832202
4761 Utot 2704347
4762 Utot 2763793
4763 Utot 2973497
4764 Utot 2731434
4765 Utot 2600865
4766 Utot 2690099
4767 Utot 2564825
4768 Utot 2767770
4769 Utot 2729063
4770 Utot 2424559
4771 Utot 2689653
4772 Utot 2605820
4773 Utot 2545800
4774 Utot 2921458
4775 Utot 2653182
4776 Utot 2876124
4777 Utot 2773698
4778 Utot 2823463
4779 Utot 2610736
4780 Utot 2662885
4781 Utot 2729972
4782 Utot 2816055
4783 Utot 2684616
4784 Utot 2560164
4785 Utot 2699183
4786 Utot 2718704
4787 Utot 2740209
4788 Utot 2677576
4789 Utot 2831414
4790 Utot 2567214
4791 Utot 2751354
4792 Utot 2833245
4793 Utot 2814619
4794 Utot 2763791
4795 Utot 2752218
4796 Utot 2800022
4797 Utot 2575651
4798 Utot 2633435
4799 Utot 2608761
4800 Utot 2808106
4801 Utot 2867441
4802 Utot 2648925
4803 Utot 2915273
4804 Utot 2630207
4805 Utot 2632688
4806 Utot 2725294
4807 Utot 2696124
4808 Utot 2770155
4809 Utot 2726356
4810 Utot 2830336
4811 Utot 2817388
4812 Utot 2553154
4813 Utot 2567098
4814 Utot 2738302
4815 Utot 2677370
4816 Utot 2771800
4817 Utot 2626528
4818 Utot 2656410
4819 Utot 2551712
4820 Utot 2633735
4821 Utot 2641765
4822 Utot 2618053
4823 Utot 2631537
4824 Utot 2808993
4825 Utot 2804457
4826 Utot 2792389
4827 Utot 2773514
4828 Utot 2747393
4829 Utot 2658887
4830 Utot 2767569
4831 Utot 2778683
4832 Utot 2753363
4833 Utot 2483766
4834 Utot 2747851
4835 Utot 2525806
4836 Utot 2862343
4837 Utot 2718125
4838 Utot 2804525
4839 Utot 2634063
4840 Utot 2678071
4841 Utot 2702394
4842 Utot 2627801
4843 Utot 2685883
4844 Utot 2806429
4845 Utot 2562013
4846 Utot 2736255
4847 Utot 2801963
4848 Utot 2569042
4849 Utot 2784931
4850 Utot 2760237
4851 Utot 2711960
4852 Utot 2710771
4853 Utot 2487914
4854 Utot 2595922
4855 Utot 2657447
4856 Utot 2844217
4857 Utot 2662295
4858 Utot 2742102
4859 Utot 2698022
4860 Utot 2647657
4861 Utot 2603197
4862 Utot 2729298
4863 Utot 2786158
4864 Utot 2521264
4865 Utot 2757347
4866 Utot 2803933
4867 Utot 2818715
4868 Utot 2529910
4869 Utot 2597507
4870 Utot 2835162
4871 Utot 2615522
4872 Utot 2958056
4873 Utot 2712950
4874 Utot 2692817
4875 Utot 2574026
4876 Utot 2730032
4877 Utot 2851192
4878 Utot 2777402
4879 Utot 2771992
4880 Utot 3010593
4881 Utot 2553883
4882 Utot 2566989
4883 Utot 2726533
4884 Utot 2789146
4885 Utot 2712141
4886 Utot 2757720
4887 Utot 2577181
4888 Utot 2654415
4889 Utot 2874467
4890 Utot 2714624
4891 Utot 2815668
4892 Utot 2620090
4893 Utot 2740833
4894 Utot 2844728
4895 Utot 2707627
4896 Utot 2610051
4897 Utot 2576742
4898 Utot 2814453
4899 Utot 2701744
4900 Utot 2779087
4901 Utot 2645625
4902 Utot 2735256
4903 Utot 2571343
4904 Utot 2694545
4905 Utot 2823338
4906 Utot 2844054
4907 Utot 2766214
4908 Utot 2644012
4909 Utot 2730432
4910 Utot 2641064
4911 Utot 2655498
4912 Utot 2506041
4913 Utot 2640930
4914 Utot 2762220
4915 Utot 2745045
4916 Utot 2719463
4917 Utot 2768777
4918 Utot 2745585
4919 Utot 2629881
4920 Utot 2609006
4921 Utot 2884434
4922 Utot 2601542
4923 Utot 2738192
4924 Utot 2851774
4925 Utot 2638948
4926 Utot 2695542
4927 Utot 2766504
4928 Utot 2830551
4929 Utot 2710429
4930 Utot 2669698
4931 Utot 2485347
4932 Utot 2534115
4933 Utot 2822011
4934 Utot 2650181
4935 Utot 2731297
4936 Utot 2746993
4937 Utot 2582250
4938 Utot 2682362
4939 Utot 2829850
4940 Utot 2646878
4941 Utot 2939391
4942 Utot 2592352
4943 Utot 2680720
4944 Utot 2649840
4945 Utot 2586564
4946 Utot 2533446
4947 Utot 2635722
4948 Utot 2860395
4949 Utot 2512661
4950 Utot 2537942
4951 Utot 2781288
4952 Utot 2708071
4953 Utot 2848864
4954 Utot 2657927
4955 Utot 2773064
4956 Utot 2704012
4957 Utot 2853170
4958 Utot 2781848
4959 Utot 2827072
4960 Utot 2478845
4961 Utot 2667515
4962 Utot 2532874
4963 Utot 2805418
4964 Utot 2911299
4965 Utot 2810289
4966 Utot 2869224
4967 Utot 2692572
4968 Utot 2866276
4969 Utot 2864244
4970 Utot 2693465
4971 Utot 2742364
4972 Utot 2709928
4973 Utot 2720425
4974 Utot 2632520
4975 Utot 2715547
4976 Utot 2490158
4977 Utot 2830387
4978 Utot 2755355
4979 Utot 2789121
4980 Utot 2662520
4981 Utot 2827446
4982 Utot 2906417
4983 Utot 2966054
4984 Utot 2888622
4985 Utot 2692740
4986 Utot 2957101
4987 Utot 2692365
4988 Utot 2747467
4989 Utot 2645584
4990 Utot 2579150
4991 Utot 2806410
4992 Utot 2628630
4993 Utot 2797670
4994 Utot 2735089
4995 Utot 2708953
4996 Utot 2851886
4997 Utot 2843873
4998 Utot 2653178
4999 Utot 2757367
5000 Utot 2680628
5001 Utot 2675396
5002 Utot 2733058
5003 Utot 2546841
5004 Utot 2696595
5005 Utot 2596859
5006 Utot 2652086
5007 Utot 2613458
5008 Utot 2524761
5009 Utot 2792088
5010 Utot 2771211
5011 Utot 2662289
5012 Utot 2797419
5013 Utot 2684854
5014 Utot 2786343
5015 Utot 2706930
5016 Utot 2727701
5017 Utot 2659745
5018 Utot 2595218
5019 Utot 2759772
5020 Utot 2737783
5021 Utot 2810459
5022 Utot 2748767
5023 Utot 2824374
5024 Utot 2800073
5025 Utot 2844548
5026 Utot 2708864
5027 Utot 2690936
5028 Utot 2722761
5029 Utot 2809753
5030 Utot 2639760
5031 Utot 2768359
5032 Utot 2664241
5033 Utot 2741359
5034 Utot 2719462
5035 Utot 2615217
5036 Utot 2939431
5037 Utot 2653563
5038 Utot 2615387
5039 Utot 2718932
5040 Utot 2758983
5041 Utot 2732561
5042 Utot 2577816
5043 Utot 2657598
5044 Utot 2633703
5045 Utot 2803923
5046 Utot 2648155
5047 Utot 2683985
5048 Utot 2566219
5049 Utot 2874889
5050 Utot 2746344
5051 Utot 2639330
5052 Utot 2746283
5053 Utot 2545677
5054 Utot 2720948
5055 Utot 2641088
5056 Utot 2734707
5057 Utot 2704532
5058 Utot 2798101
5059 Utot 2802007
5060 Utot 2714615
5061 Utot 2594246
5062 Utot 2711368
5063 Utot 2650525
5064 Utot 2790925
5065 Utot 2602019
5066 Utot 2783712
5067 Utot 2660521
5068 Utot 2723648
5069 Utot 2727118
5070 Utot 2545774
5071 Utot 2709330
5072 Utot 2585800
5073 Utot 2622411
5074 Utot 2668514
5075 Utot 2668981
5076 Utot 2448507
5077 Utot 2633936
5078 Utot 2642986
5079 Utot 2497404
5080 Utot 2566086
5081 Utot 2586739
5082 Utot 2806347
5083 Utot 2787356
5084 Utot 2750563
5085 Utot 2587243
5086 Utot 2623447
5087 Utot 2786154
5088 Utot 2932724
5089 Utot 2728862
5090 Utot 2662318
5091 Utot 2799694
5092 Utot 2814097
5093 Utot 2639105
5094 Utot 2633445
5095 Utot 2732104
5096 Utot 2711124
5097 Utot 2836168
5098 Utot 2759579
5099 Utot 2787042
5100 Utot 2673497
5101 Utot 2625233
5102 Utot 2470443
5103 Utot 2684699
5104 Utot 2738428
5105 Utot 2620887
5106 Utot 2667398
5107 Utot 2643249
5108 Utot 2706418
5109 Utot 2711662
5110 Utot 2685223
5111 Utot 2681429
5112 Utot 2652006
5113 Utot 2727961
5114 Utot 2733489
5115 Utot 2666753
5116 Utot 2766542
5117 Utot 2583957
5118 Utot 2732216
5119 Utot 2755673
5120 Utot 2714765
5121 Utot 2852052
5122 Utot 2744357
5123 Utot 2574724
5124 Utot 2697668
5125 Utot 2733594
5126 Utot 2754275
5127 Utot 2595779
5128 Utot 2796795
5129 Utot 2727617
5130 Utot 2733653
5131 Utot 2516223
5132 Utot 2602482
5133 Utot 2741341
5134 Utot 2533661
5135 Utot 2702713
5136 Utot 2747665
5137 Utot 2655112
5138 Utot 2697003
5139 Utot 2670365
5140 Utot 2765391
5141 Utot 2778727
5142 Utot 2652697
5143 Utot 2712349
5144 Utot 2733199
5145 Utot 2860244
5146 Utot 2787156
5147 Utot 2602563
5148 Utot 2658436
5149 Utot 2711886
5150 Utot 2823882
5151 Utot 2621014
5152 Utot 2775388
5153 Utot 2685084
5154 Utot 2719833
5155 Utot 2584085
5156 Utot 2594714
5157 Utot 2602347
5158 Utot 2429258
5159 Utot 2698051
5160 Utot 2614758
5161 Utot 2710149
5162 Utot 2634461
5163 Utot 2639966
5164 Utot 2973297
5165 Utot 2545605
5166 Utot 2594516
5167 Utot 2705149
5168 Utot 2771718
5169 Utot 2731670
5170 Utot 2693884
5171 Utot 2617383
5172 Utot 2814305
5173 Utot 2691853
5174 Utot 2688569
5175 Utot 2633808
5176 Utot 2967011
5177 Utot 2624203
5178 Utot 2701536
5179 Utot 2671904
5180 Utot 2502174
5181 Utot 2719066
5182 Utot 2874587
5183 Utot 2828385
5184 Utot 2703182
5185 Utot 2866398
5186 Utot 2885631
5187 Utot 2914611
5188 Utot 3036907
5189 Utot 2764454
5190 Utot 2774009
5191 Utot 2744582
5192 Utot 2734794
5193 Utot 2731853
5194 Utot 2763049
5195 Utot 2563146
5196 Utot 2851286
5197 Utot 2616237
5198 Utot 2710496
5199 Utot 2821888
5200 Utot 2537216
5201 Utot 2977014
5202 Utot 2573835
5203 Utot 2672205
5204 Utot 2867131
5205 Utot 2677858
5206 Utot 2757245
5207 Utot 2732467
5208 Utot 2631403
5209 Utot 2753751
5210 Utot 2663802
5211 Utot 2607231
5212 Utot 2752277
5213 Utot 2833752
5214 Utot 2993158
5215 Utot 2973238
5216 Utot 2749957
5217 Utot 2862211
5218 Utot 2663396
5219 Utot 2552596
5220 Utot 2637548
5221 Utot 2507926
5222 Utot 2570363
5223 Utot 2895708
5224 Utot 2834744
5225 Utot 2731904
5226 Utot 2801125
5227 Utot 2985525
5228 Utot 2688029
5229 Utot 2595668
5230 Utot 2757346
5231 Utot 2838080
5232 Utot 2502117
5233 Utot 2644108
5234 Utot 2720455
5235 Utot 2797067
5236 Utot 2611892
5237 Utot 2656580
5238 Utot 2859787
5239 Utot 2524943
5240 Utot 2787830
5241 Utot 2825597
5242 Utot 2751562
5243 Utot 2744388
5244 Utot 2635338
5245 Utot 2792290
5246 Utot 2810036
5247 Utot 2706138
5248 Utot 2662380
5249 Utot 2632476
5250 Utot 2851503
5251 Utot 2752442
5252 Utot 2703995
5253 Utot 3148424
5254 Utot 2522470
5255 Utot 2720759
5256 Utot 2808013
5257 Utot 2694200
5258 Utot 2705318
5259 Utot 2676683
5260 Utot 2775811
5261 Utot 2614708
5262 Utot 2549694
5263 Utot 2860675
5264 Utot 2665607
5265 Utot 2872577
5266 Utot 2523975
5267 Utot 2622216
5268 Utot 2626619
5269 Utot 2606971
5270 Utot 2803584
5271 Utot 2537369
5272 Utot 2676118
5273 Utot 2791317
5274 Utot 2623475
5275 Utot 2645164
5276 Utot 2623354
5277 Utot 2556224
5278 Utot 2656443
5279 Utot 2599749
5280 Utot 2737952
5281 Utot 2731299
5282 Utot 2685767
5283 Utot 2637394
5284 Utot 2887053
5285 Utot 2839037
5286 Utot 2751045
5287 Utot 2959497
5288 Utot 2553743
5289 Utot 2716237
5290 Utot 2530087
5291 Utot 2721567
5292 Utot 2688066
5293 Utot 2600642
5294 Utot 2872496
5295 Utot 2836376
5296 Utot 2638283
5297 Utot 2715386
5298 Utot 2598152
5299 Utot 2779082
5300 Utot 2712209
5301 Utot 2744080
5302 Utot 2543065
5303 Utot 2933083
5304 Utot 2644885
5305 Utot 2763907
5306 Utot 2749115
5307 Utot 2572708
5308 Utot 2759436
5309 Utot 2592992
5310 Utot 2618220
5311 Utot 2804383
5312 Utot 2691332
5313 Utot 2875238
5314 Utot 2466366
5315 Utot 2894485
5316 Utot 2625720
5317 Utot 2746130
5318 Utot 2682079
5319 Utot 2725660
5320 Utot 2729949
5321 Utot 2611315
5322 Utot 2621157
5323 Utot 2714098
5324 Utot 2782738
5325 Utot 2674547
5326 Utot 2663945
5327 Utot 2599251
5328 Utot 2651464
5329 Utot 2669726
5330 Utot 2845658
5331 Utot 2601089
5332 Utot 2680422
5333 Utot 2741693
5334 Utot 2810676
5335 Utot 2621642
5336 Utot 2894869
5337 Utot 2601697
5338 Utot 2659558
5339 Utot 2656279
5340 Utot 2628510
5341 Utot 2756804
5342 Utot 2635634
5343 Utot 2655326
5344 Utot 2683517
5345 Utot 2735196
5346 Utot 2667660
5347 Utot 2746317
5348 Utot 2781700
5349 Utot 2687696
5350 Utot 2621388
5351 Utot 2757228
5352 Utot 2688220
5353 Utot 2731060
5354 Utot 2623969
5355 Utot 2726379
5356 Utot 2728422
5357 Utot 2772373
5358 Utot 2680478
5359 Utot 2726932
5360 Utot 2703974
5361 Utot 2801227
5362 Utot 2648633
5363 Utot 2517237
5364 Utot 2878323
5365 Utot 2445408
5366 Utot 2456419
5367 Utot 2589496
5368 Utot 2813770
5369 Utot 2763459
5370 Utot 2684519
5371 Utot 2593472
5372 Utot 2678316
5373 Utot 2684542
5374 Utot 2837004
5375 Utot 2655061
5376 Utot 2587417
5377 Utot 2636316
5378 Utot 2768472
5379 Utot 2835496
5380 Utot 2580163
5381 Utot 2607215
5382 Utot 2649420
5383 Utot 2793548
5384 Utot 2519503
5385 Utot 2710883
5386 Utot 2880496
5387 Utot 2742498
5388 Utot 2719838
5389 Utot 2751294
5390 Utot 2700886
5391 Utot 2509874
5392 Utot 2891623
5393 Utot 3053199
5394 Utot 2778717
5395 Utot 2786939
5396 Utot 2674049
5397 Utot 2686490
5398 Utot 2658177
5399 Utot 2718833
5400 Utot 2729907
5401 Utot 2896883
5402 Utot 2804973
5403 Utot 2840984
5404 Utot 2723915
5405 Utot 2634027
5406 Utot 2660567
5407 Utot 2827080
5408 Utot 2621533
5409 Utot 2827377
5410 Utot 2616659
5411 Utot 2757834
5412 Utot 2562661
5413 Utot 2647577
5414 Utot 2571766
5415 Utot 2797331
5416 Utot 2554645
5417 Utot 2601833
5418 Utot 2769871
5419 Utot 2586010
5420 Utot 2720176
5421 Utot 2694741
5422 Utot 2733119
5423 Utot 2755331
5424 Utot 2880553
5425 Utot 2775937
5426 Utot 2863366
5427 Utot 2684923
5428 Utot 2729890
5429 Utot 2753682
5430 Utot 2691616
5431 Utot 2812475
5432 Utot 2719349
5433 Utot 2595511
5434 Utot 2646926
5435 Utot 2675917
5436 Utot 2727656
5437 Utot 2516890
5438 Utot 2708073
5439 Utot 2776910
5440 Utot 2568983
5441 Utot 2697465
5442 Utot 2753242
5443 Utot 2722149
5444 Utot 2854797
5445 Utot 2681885
5446 Utot 2662286
5447 Utot 2767751
5448 Utot 2783414
5449 Utot 2765571
5450 Utot 2891564
5451 Utot 2804073
5452 Utot 2689292
5453 Utot 2767975
5454 Utot 2607332
5455 Utot 2578136
5456 Utot 2808089
5457 Utot 2762620
5458 Utot 2832921
5459 Utot 2792300
5460 Utot 2644809
5461 Utot 2693580
5462 Utot 2757604
5463 Utot 2837748
5464 Utot 2787851
5465 Utot 2664497
5466 Utot 2787269
5467 Utot 2861676
5468 Utot 2796026
5469 Utot 2631447
5470 Utot 2743715
5471 Utot 2623561
5472 Utot 2661561
5473 Utot 2690852
5474 Utot 2897202
5475 Utot 2731667
5476 Utot 2753156
5477 Utot 3022642
5478 Utot 2745441
5479 Utot 2471280
5480 Utot 2584787
5481 Utot 2717234
5482 Utot 2775598
5483 Utot 2682496
5484 Utot 2726797
5485 Utot 2808859
5486 Utot 2803585
5487 Utot 2550085
5488 Utot 2605771
5489 Utot 2689918
5490 Utot 2895083
5491 Utot 2641762
5492 Utot 2981759
5493 Utot 2764317
5494 Utot 2746093
5495 Utot 2658885
5496 Utot 2888708
5497 Utot 2703819
5498 Utot 2897447
5499 Utot 2806850
5500 Utot 2557060
5501 Utot 2623681
5502 Utot 2696465
5503 Utot 2570542
5504 Utot 2848113
5505 Utot 2874262
5506 Utot 2763957
5507 Utot 2686165
5508 Utot 2756099
5509 Utot 2682513
5510 Utot 2713746
5511 Utot 2559199
5512 Utot 2751877
5513 Utot 2714410
5514 Utot 2845261
5515 Utot 2753272
5516 Utot 2850011
5517 Utot 2733694
5518 Utot 2797211
5519 Utot 2465778
5520 Utot 2763939
5521 Utot 2664376
5522 Utot 2700636
5523 Utot 2691882
5524 Utot 2674608
5525 Utot 2483737
5526 Utot 2868338
5527 Utot 2709237
5528 Utot 2857782
5529 Utot 2615571
5530 Utot 2531509
5531 Utot 2710764
5532 Utot 2782998
5533 Utot 2926150
5534 Utot 2754676
5535 Utot 2808781
5536 Utot 2582277
5537 Utot 2646136
5538 Utot 2809139
5539 Utot 2853216
5540 Utot 2746019
5541 Utot 2704535
5542 Utot 2568224
5543 Utot 2624665
5544 Utot 2731060
5545 Utot 2691674
5546 Utot 2890307
5547 Utot 2695686
5548 Utot 2925967
5549 Utot 2626723
5550 Utot 2628104
5551 Utot 2935142
5552 Utot 2688391
5553 Utot 2612740
5554 Utot 2844730
5555 Utot 2669724
5556 Utot 2522874
5557 Utot 2761667
5558 Utot 2768535
5559 Utot 2795829
5560 Utot 2819595
5561 Utot 2752658
5562 Utot 2780259
5563 Utot 2762771
5564 Utot 2781942
5565 Utot 2607630
5566 Utot 2550429
5567 Utot 2668575
5568 Utot 2607475
5569 Utot 2773187
5570 Utot 2509616
5571 Utot 2832098
5572 Utot 2691244
5573 Utot 2746114
5574 Utot 2908116
5575 Utot 2681385
5576 Utot 2686371
5577 Utot 2664078
5578 Utot 2773177
5579 Utot 2684510
5580 Utot 2608941
5581 Utot 2688938
5582 Utot 2757072
5583 Utot 2550876
5584 Utot 2707931
5585 Utot 2810123
5586 Utot 2837956
5587 Utot 2658525
5588 Utot 2795680
5589 Utot 2715992
5590 Utot 2957495
5591 Utot 2874906
5592 Utot 2823086
5593 Utot 3024529
5594 Utot 2663958
5595 Utot 2871983
5596 Utot 2701664
5597 Utot 2643398
5598 Utot 2618641
5599 Utot 2632706
5600 Utot 2669623
5601 Utot 2649450
5602 Utot 2800361
5603 Utot 2670539
5604 Utot 2766762
5605 Utot 2624933
5606 Utot 2740342
5607 Utot 2736872
5608 Utot 2556811
5609 Utot 2697666
5610 Utot 2672723
5611 Utot 2638321
5612 Utot 2738622
5613 Utot 2789181
5614 Utot 2609340
5615 Utot 2965786
5616 Utot 2834541
5617 Utot 2631711
5618 Utot 2811008
5619 Utot 2755798
5620 Utot 2574217
5621 Utot 2822174
5622 Utot 2696541
5623 Utot 2708335
5624 Utot 2792030
5625 Utot 2643390
5626 Utot 2861599
5627 Utot 2823422
5628 Utot 2607139
5629 Utot 2770890
5630 Utot 2840249
5631 Utot 2600569
5632 Utot 2649715
5633 Utot 2710758
5634 Utot 2553373
5635 Utot 2652050
5636 Utot 2654557
5637 Utot 2761122
5638 Utot 2835910
5639 Utot 2685328
5640 Utot 2770258
5641 Utot 2753997
5642 Utot 2642830
5643 Utot 2511096
5644 Utot 3015007
5645 Utot 2572904
5646 Utot 2758510
5647 Utot 2627333
5648 Utot 2701840
5649 Utot 2634713
5650 Utot 2697737
5651 Utot 2752531
5652 Utot 2692813
5653 Utot 2777650
5654 Utot 2748306
5655 Utot 2881651
5656 Utot 2667416
5657 Utot 2626772
5658 Utot 2597519
5659 Utot 2724538
5660 Utot 2773571
5661 Utot 2581907
5662 Utot 2696127
5663 Utot 2735594
5664 Utot 2656697
5665 Utot 2712478
5666 Utot 2583618
5667 Utot 2801235
5668 Utot 2631162
5669 Utot 2562956
5670 Utot 2844028
5671 Utot 2534492
5672 Utot 2828447
5673 Utot 2667590
5674 Utot 2947796
5675 Utot 2776001
5676 Utot 2809097
5677 Utot 2721037
5678 Utot 2833228
5679 Utot 2794011
5680 Utot 2951795
5681 Utot 2679942
5682 Utot 2687423
5683 Utot 2622227
5684 Utot 2877315
5685 Utot 2564544
5686 Utot 2636773
5687 Utot 2768592
5688 Utot 2754191
5689 Utot 2805423
5690 Utot 2823598
5691 Utot 2601223
5692 Utot 2824559
5693 Utot 2987252
5694 Utot 2745537
5695 Utot 2846564
5696 Utot 2816765
5697 Utot 2582796
5698 Utot 2641269
5699 Utot 2868002
5700 Utot 2804325
5701 Utot 2780396
5702 Utot 2506759
5703 Utot 2594574
5704 Utot 2566407
5705 Utot 2646229
5706 Utot 2715361
5707 Utot 2786398
5708 Utot 2706628
5709 Utot 2557857
5710 Utot 2769701
5711 Utot 2755335
5712 Utot 2692577
5713 Utot 2677897
5714 Utot 2710352
5715 Utot 2774885
5716 Utot 2767258
5717 Utot 2540577
5718 Utot 2549656
5719 Utot 2759254
5720 Utot 2844510
5721 Utot 2631772
5722 Utot 2875885
5723 Utot 2633275
5724 Utot 2807151
5725 Utot 2656057
5726 Utot 2807436
5727 Utot 2600502
5728 Utot 2669585
5729 Utot 2855471
5730 Utot 2561373
5731 Utot 2916857
5732 Utot 2836627
5733 Utot 2936869
5734 Utot 2762643
5735 Utot 2799061
5736 Utot 2650494
5737 Utot 2848987
5738 Utot 2718009
5739 Utot 2771992
5740 Utot 2640341
5741 Utot 2820604
5742 Utot 2800894
5743 Utot 2526562
5744 Utot 2612556
5745 Utot 2843441
5746 Utot 2546143
5747 Utot 2628224
5748 Utot 2741607
5749 Utot 2589333
5750 Utot 2676333
5751 Utot 2767203
5752 Utot 2879230
5753 Utot 2662175
5754 Utot 2674436
5755 Utot 2833844
5756 Utot 2829123
5757 Utot 2796591
5758 Utot 2680328
5759 Utot 2698753
5760 Utot 2914122
5761 Utot 2813104
5762 Utot 2743056
5763 Utot 2667960
5764 Utot 2507145
5765 Utot 2774670
5766 Utot 2628820
5767 Utot 2626328
5768 Utot 2443387
5769 Utot 2723471
5770 Utot 2615568
5771 Utot 2811285
5772 Utot 2739468
5773 Utot 2658978
5774 Utot 2627247
5775 Utot 2708708
5776 Utot 2632574
5777 Utot 2595763
5778 Utot 2711776
5779 Utot 2566884
5780 Utot 2669193
5781 Utot 2547345
5782 Utot 2957250
5783 Utot 2646682
5784 Utot 2709488
5785 Utot 2938189
5786 Utot 2652075
5787 Utot 2766170
5788 Utot 2616373
5789 Utot 2715453
5790 Utot 2608725
5791 Utot 2759738
5792 Utot 2678671
5793 Utot 2481889
5794 Utot 2620692
5795 Utot 2640847
5796 Utot 2630763
5797 Utot 2637929
5798 Utot 2681577
5799 Utot 2688861
5800 Utot 2580852
5801 Utot 2721692
5802 Utot 2594174
5803 Utot 2746326
5804 Utot 2616919
5805 Utot 2855489
5806 Utot 2665886
5807 Utot 2854168
5808 Utot 2832211
5809 Utot 2699672
5810 Utot 2601929
5811 Utot 2692439
5812 Utot 2773628
5813 Utot 2621067
5814 Utot 2800516
5815 Utot 2829183
5816 Utot 2898535
5817 Utot 2761109
5818 Utot 2877920
5819 Utot 2775882
5820 Utot 2651048
5821 Utot 2833348
5822 Utot 2860670
5823 Utot 2730567
5824 Utot 2667838
5825 Utot 2577141
5826 Utot 2613896
5827 Utot 2644557
5828 Utot 2511099
5829 Utot 2750256
5830 Utot 2810868
5831 Utot 2769013
5832 Utot 2540226
5833 Utot 2816826
5834 Utot 2755761
5835 Utot 2719202
5836 Utot 2594279
5837 Utot 2716002
5838 Utot 2860087
5839 Utot 2583519
5840 Utot 2669107
5841 Utot 2834538
5842 Utot 2874206
5843 Utot 2865933
5844 Utot 2823461
5845 Utot 2672591
5846 Utot 2668410
5847 Utot 2569717
5848 Utot 2740100
5849 Utot 2882452
5850 Utot 2791133
5851 Utot 2731880
5852 Utot 2660243
5853 Utot 2640287
5854 Utot 2779703
5855 Utot 2768754
5856 Utot 2758094
5857 Utot 2725061
5858 Utot 2768012
5859 Utot 2646409
5860 Utot 2643537
5861 Utot 2843722
5862 Utot 2529821
5863 Utot 2705273
5864 Utot 2658095
5865 Utot 2968090
5866 Utot 2887427
5867 Utot 2617853
5868 Utot 2876410
5869 Utot 2762279
5870 Utot 2783579
5871 Utot 2793363
5872 Utot 2661563
5873 Utot 2612241
5874 Utot 2818502
5875 Utot 2745441
5876 Utot 2880584
5877 Utot 2729641
5878 Utot 2705398
5879 Utot 2810558
5880 Utot 2684588
5881 Utot 2814721
5882 Utot 2589228
5883 Utot 2671524
5884 Utot 2715017
5885 Utot 2673684
5886 Utot 2721442
5887 Utot 2628001
5888 Utot 2748128
5889 Utot 2787404
5890 Utot 2720509
5891 Utot 2661126
5892 Utot 2783058
5893 Utot 2802864
5894 Utot 2656264
5895 Utot 2700234
5896 Utot 2700710
5897 Utot 2759034
5898 Utot 2735337
5899 Utot 2781204
5900 Utot 2494406
5901 Utot 2623503
5902 Utot 2546938
5903 Utot 2777956
5904 Utot 2718620
5905 Utot 2723082
5906 Utot 2682422
5907 Utot 2751457
5908 Utot 2775872
5909 Utot 2565417
5910 Utot 2732111
5911 Utot 2649817
5912 Utot 2698684
5913 Utot 2709260
5914 Utot 2629994
5915 Utot 2598215
5916 Utot 2643623
5917 Utot 2769529
5918 Utot 2739340
5919 Utot 2691008
5920 Utot 2696231
5921 Utot 2851709
5922 Utot 2805272
5923 Utot 2911538
5924 Utot 2975963
5925 Utot 2573647
5926 Utot 2867993
5927 Utot 2575628
5928 Utot 2808186
5929 Utot 2872322
5930 Utot 2705820
5931 Utot 2621465
5932 Utot 2839687
5933 Utot 2925559
5934 Utot 2586013
5935 Utot 2717838
5936 Utot 2490631
5937 Utot 2706516
5938 Utot 2660981
5939 Utot 2636615
5940 Utot 2588768
5941 Utot 2709934
5942 Utot 2884903
5943 Utot 2927179
5944 Utot 2687338
5945 Utot 2615445
5946 Utot 2849257
5947 Utot 2588475
5948 Utot 2613904
5949 Utot 2904550
5950 Utot 2555919
5951 Utot 2689659
5952 Utot 2708702
5953 Utot 2694583
5954 Utot 2491457
5955 Utot 2768282
5956 Utot 2906500
5957 Utot 2747697
5958 Utot 2768204
5959 Utot 2700234
5960 Utot 2633497
5961 Utot 2770693
5962 Utot 2672833
5963 Utot 2723042
5964 Utot 2924281
5965 Utot 2863001
5966 Utot 2874627
5967 Utot 2670810
5968 Utot 2719862
5969 Utot 2785003
5970 Utot 2540306
5971 Utot 2783426
5972 Utot 2669585
5973 Utot 2568397
5974 Utot 2792389
5975 Utot 2772962
5976 Utot 2699913
5977 Utot 2779627
5978 Utot 2935339
5979 Utot 2621031
5980 Utot 2663432
5981 Utot 2926267
5982 Utot 2793546
5983 Utot 2794422
5984 Utot 2585590
5985 Utot 2627374
5986 Utot 2747314
5987 Utot 2833193
5988 Utot 2765407
5989 Utot 2666963
5990 Utot 2588557
5991 Utot 2505936
5992 Utot 2604114
5993 Utot 2803598
5994 Utot 2836709
5995 Utot 2657784
5996 Utot 2662449
5997 Utot 2651585
5998 Utot 2688878
5999 Utot 2532054
6000 Utot 2913027
6001 Ntot 2818504
6002 Ntot 2803520
6003 Ntot 2734225
6004 Ntot 2585149
6005 Ntot 2708289
6006 Ntot 2871926
6007 Ntot 2816506
6008 Ntot 2762413
6009 Ntot 2514710
6010 Ntot 2528273
6011 Ntot 2796424
6012 Ntot 2835261
6013 Ntot 2623847
6014 Ntot 2942375
6015 Ntot 2895388
6016 Ntot 2843503
6017 Ntot 2762821
6018 Ntot 2869393
6019 Ntot 2926548
6020 Ntot 2824462
6021 Ntot 2796629
6022 Ntot 2770412
6023 Ntot 2734882
6024 Ntot 2785120
6025 Ntot 2802230
6026 Ntot 2687866
6027 Ntot 2657488
6028 Ntot 2848014
6029 Ntot 2713703
6030 Ntot 2734892
6031 Ntot 2780026
6032 Ntot 2770790
6033 Ntot 2854489
6034 Ntot 2705212
6035 Ntot 2625939
6036 Ntot 2809443
6037 Ntot 2859155
6038 Ntot 2774719
6039 Ntot 2949221
6040 Ntot 2669491
6041 Ntot 2959830
6042 Ntot 2865597
6043 Ntot 2817691
6044 Ntot 2631133
6045 Ntot 2773662
6046 Ntot 2961428
6047 Ntot 2543012
6048 Ntot 2689375
6049 Ntot 2700642
6050 Ntot 2653869
6051 Ntot 2755666
6052 Ntot 2508602
6053 Ntot 2767413
6054 Ntot 2844307
6055 Ntot 2853899
6056 Ntot 3015758
6057 Ntot 2873995
6058 Ntot 2735807
6059 Ntot 2831263
6060 Ntot 2910642
6061 Ntot 2705843
6062 Ntot 2520667
6063 Ntot 2829352
6064 Ntot 2648458
6065 Ntot 2807023
6066 Ntot 2787346
6067 Ntot 2727563
6068 Ntot 2841917
6069 Ntot 2719943
6070 Ntot 2699398
6071 Ntot 2790487
6072 Ntot 2881089
6073 Ntot 2849091
6074 Ntot 2901871
6075 Ntot 2853538
6076 Ntot 2601957
6077 Ntot 2643708
6078 Ntot 2808964
6079 Ntot 2814278
6080 Ntot 2904527
6081 Ntot 2757282
6082 Ntot 2843489
6083 Ntot 2680370
6084 Ntot 2781945
6085 Ntot 2861692
6086 Ntot 2624852
6087 Ntot 2820815
6088 Ntot 2828404
6089 Ntot 2650378
6090 Ntot 2740269
6091 Ntot 2745685
6092 Ntot 2875332
6093 Ntot 2670016
6094 Ntot 2876159
6095 Ntot 2864742
6096 Ntot 2724295
6097 Ntot 2876460
6098 Ntot 2598522
6099 Ntot 2737696
6100 Ntot 2779794
6101 Ntot 2787618
6102 Ntot 2936920
6103 Ntot 2655143
6104 Ntot 2778344
6105 Ntot 2685599
6106 Ntot 2750149
6107 Ntot 2906786
6108 Ntot 2680333
6109 Ntot 2871820
6110 Ntot 2725537
6111 Ntot 2809534
6112 Ntot 2835257
6113 Ntot 2635709
6114 Ntot 2720595
6115 Ntot 2795574
6116 Ntot 2680221
6117 Ntot 2504376
6118 Ntot 2771722
6119 Ntot 2666125
6120 Ntot 2854842
6121 Ntot 2738761
6122 Ntot 2649712
6123 Ntot 2759683
6124 Ntot 2865638
6125 Ntot 2670673
6126 Ntot 2864764
6127 Ntot 2845522
6128 Ntot 2770076
6129 Ntot 2689113
6130 Ntot 2625977
6131 Ntot 2713019
6132 Ntot 2598302
6133 Ntot 2944630
6134 Ntot 2809478
6135 Ntot 2922897
6136 Ntot 2690468
6137 Ntot 2795320
6138 Ntot 2727181
6139 Ntot 2783291
6140 Ntot 2687036
6141 Ntot 2775750
6142 Ntot 2724802
6143 Ntot 2667988
6144 Ntot 2784797
6145 Ntot 2807183
6146 Ntot 2709664
6147 Ntot 2672312
6148 Ntot 2684252
6149 Ntot 2882497
6150 Ntot 2730317
6151 Ntot 2823545
6152 Ntot 2603002
6153 Ntot 2873054
6154 Ntot 2668528
6155 Ntot 2755064
6156 Ntot 2853635
6157 Ntot 2592847
6158 Ntot 2694950
6159 Ntot 2748479
6160 Ntot 2674640
6161 Ntot 2668683
6162 Ntot 2660100
6163 Ntot 2683179
6164 Ntot 2826551
6165 Ntot 2513969
6166 Ntot 2849092
6167 Ntot 2638633
6168 Ntot 2771692
6169 Ntot 2700347
6170 Ntot 2686415
6171 Ntot 2837876
6172 Ntot 2784153
6173 Ntot 2760957
6174 Ntot 2935252
6175 Ntot 2614677
6176 Ntot 2857894
6177 Ntot 2664785
6178 Ntot 2765481
6179 Ntot 2625623
6180 Ntot 2649606
6181 Ntot 2620090
6182 Ntot 2743574
6183 Ntot 2908420
6184 Ntot 2809310
6185 Ntot 2581830
6186 Ntot 2919489
6187 Ntot 2730750
6188 Ntot 2683799
6189 Ntot 2890007
6190 Ntot 2726140
6191 Ntot 2715000
6192 Ntot 2626972
6193 Ntot 2641213
6194 Ntot 2879278
6195 Ntot 2744836
6196 Ntot 2871207
6197 Ntot 2626782
6198 Ntot 2708013
6199 Ntot 2863372
6200 Ntot 2781345
6201 Ntot 2789167
6202 Ntot 2647954
6203 Ntot 2674049
6204 Ntot 2763492
6205 Ntot 2842076
6206 Ntot 2750855
6207 Ntot 2754022
6208 Ntot 2579759
6209 Ntot 2661004
6210 Ntot 2475435
6211 Ntot 2640538
6212 Ntot 2713159
6213 Ntot 2816581
6214 Ntot 2773261
6215 Ntot 2565332
6216 Ntot 2625555
6217 Ntot 2702721
6218 Ntot 2691654
6219 Ntot 2708713
6220 Ntot 2762770
6221 Ntot 2828239
6222 Ntot 2662489
6223 Ntot 2610096
6224 Ntot 2781385
6225 Ntot 2880984
6226 Ntot 2670304
6227 Ntot 2717867
6228 Ntot 2803525
6229 Ntot 2763066
6230 Ntot 2897972
6231 Ntot 2867519
6232 Ntot 2823856
6233 Ntot 2607798
6234 Ntot 2668407
6235 Ntot 2892477
6236 Ntot 2832274
6237 Ntot 2854706
6238 Ntot 2759090
6239 Ntot 2658628
6240 Ntot 2775330
6241 Ntot 2749674
6242 Ntot 2910350
6243 Ntot 2754142
6244 Ntot 2794477
6245 Ntot 2870695
6246 Ntot 2873719
6247 Ntot 2705687
6248 Ntot 2809772
6249 Ntot 2836781
6250 Ntot 2538824
6251 Ntot 2747176
6252 Ntot 2748245
6253 Ntot 2750170
6254 Ntot 2683523
6255 Ntot 2932883
6256 Ntot 2706576
6257 Ntot 2754825
6258 Ntot 2716348
6259 Ntot 2747711
6260 Ntot 2599961
6261 Ntot 2812274
6262 Ntot 2675724
6263 Ntot 2840989
6264 Ntot 2727154
6265 Ntot 2801603
6266 Ntot 2727825
6267 Ntot 2760606
6268 Ntot 3088118
6269 Ntot 2709710
6270 Ntot 2791661
6271 Ntot 2603433
6272 Ntot 2657316
6273 Ntot 2718281
6274 Ntot 2678124
6275 Ntot 2752412
6276 Ntot 2731415
6277 Ntot 2763699
6278 Ntot 2694213
6279 Ntot 2894491
6280 Ntot 2606161
6281 Ntot 2933686
6282 Ntot 2665498
6283 Ntot 2729763
6284 Ntot 2869339
6285 Ntot 2888588
6286 Ntot 2613590
6287 Ntot 2768613
6288 Ntot 2788426
6289 Ntot 2816789
6290 Ntot 2816780
6291 Ntot 2864152
6292 Ntot 2977362
6293 Ntot 2855842
6294 Ntot 2575396
6295 Ntot 2779169
6296 Ntot 2762818
6297 Ntot 2642594
6298 Ntot 2742383
6299 Ntot 2832907
6300 Ntot 2810874
6301 Ntot 2556614
6302 Ntot 2851641
6303 Ntot 2840718
6304 Ntot 2813427
6305 Ntot 2840239
6306 Ntot 2915306
6307 Ntot 2807329
6308 Ntot 2833048
6309 Ntot 2541531
6310 Ntot 2978410
6311 Ntot 2844330
6312 Ntot 2577429
6313 Ntot 2900548
6314 Ntot 2771900
6315 Ntot 2710718
6316 Ntot 2740649
6317 Ntot 2794501
6318 Ntot 3093187
6319 Ntot 2776216
6320 Ntot 2677309
6321 Ntot 2946432
6322 Ntot 2770078
6323 Ntot 2781197
6324 Ntot 3034501
6325 Ntot 2741341
6326 Ntot 2879597
6327 Ntot 2610508
6328 Ntot 2657502
6329 Ntot 2694594
6330 Ntot 2955392
6331 Ntot 2943540
6332 Ntot 2826395
6333 Ntot 2876526
6334 Ntot 2738679
6335 Ntot 2692948
6336 Ntot 2779071
6337 Ntot 2712069
6338 Ntot 2830176
6339 Ntot 2736903
6340 Ntot 2986270
6341 Ntot 2544552
6342 Ntot 2637869
6343 Ntot 2757521
6344 Ntot 2576605
6345 Ntot 2827835
6346 Ntot 2716441
6347 Ntot 2924567
6348 Ntot 2991387
6349 Ntot 2794880
6350 Ntot 3026810
6351 Ntot 2767756
6352 Ntot 2896227
6353 Ntot 2793038
6354 Ntot 2994545
6355 Ntot 2769896
6356 Ntot 2760865
6357 Ntot 2775000
6358 Ntot 2754383
6359 Ntot 2990402
6360 Ntot 2772673
6361 Ntot 2709070
6362 Ntot 2774599
6363 Ntot 2743888
6364 Ntot 2746802
6365 Ntot 2800083
6366 Ntot 2747956
6367 Ntot 2752925
6368 Ntot 2796565
6369 Ntot 2586060
6370 Ntot 2930925
6371 Ntot 3013306
6372 Ntot 2873803
6373 Ntot 2779298
6374 Ntot 2647766
6375 Ntot 2872833
6376 Ntot 2597525
6377 Ntot 2569074
6378 Ntot 2783752
6379 Ntot 2829736
6380 Ntot 2686669
6381 Ntot 2846576
6382 Ntot 2690574
6383 Ntot 2923858
6384 Ntot 2769567
6385 Ntot 2879578
6386 Ntot 2798098
6387 Ntot 2761407
6388 Ntot 2787233
6389 Ntot 2959268
6390 Ntot 2742579
6391 Ntot 2699673
6392 Ntot 2677581
6393 Ntot 2866555
6394 Ntot 2823468
6395 Ntot 2645461
6396 Ntot 2581263
6397 Ntot 2773654
6398 Ntot 2896920
6399 Ntot 2747275
6400 Ntot 2672025
6401 Ntot 2756951
6402 Ntot 2644427
6403 Ntot 2757859
6404 Ntot 2853448
6405 Ntot 2781450
6406 Ntot 2775031
6407 Ntot 2581669
6408 Ntot 2662551
6409 Ntot 2791101
6410 Ntot 2603634
6411 Ntot 2805355
6412 Ntot 2642094
6413 Ntot 2694856
6414 Ntot 2831684
6415 Ntot 2674803
6416 Ntot 2962421
6417 Ntot 2638812
6418 Ntot 2804359
6419 Ntot 2837154
6420 Ntot 2751971
6421 Ntot 2734357
6422 Ntot 2778230
6423 Ntot 2597422
6424 Ntot 2687528
6425 Ntot 2773364
6426 Ntot 2693157
6427 Ntot 2747038
6428 Ntot 2653218
6429 Ntot 2665293
6430 Ntot 2737304
6431 Ntot 2760736
6432 Ntot 2804660
6433 Ntot 2724152
6434 Ntot 2754617
6435 Ntot 2778915
6436 Ntot 2775921
6437 Ntot 2648192
6438 Ntot 2747278
6439 Ntot 2598651
6440 Ntot 2808963
6441 Ntot 2848147
6442 Ntot 2772652
6443 Ntot 2781975
6444 Ntot 2540505
6445 Ntot 2797754
6446 Ntot 2775407
6447 Ntot 2789983
6448 Ntot 2722463
6449 Ntot 2933286
6450 Ntot 2652222
6451 Ntot 2690166
6452 Ntot 2791656
6453 Ntot 2880067
6454 Ntot 2673779
6455 Ntot 2904499
6456 Ntot 2709655
6457 Ntot 2738891
6458 Ntot 2727857
6459 Ntot 2693053
6460 Ntot 3066683
6461 Ntot 2827974
6462 Ntot 2622678
6463 Ntot 2870783
6464 Ntot 2699440
6465 Ntot 2742024
6466 Ntot 2781336
6467 Ntot 2781415
6468 Ntot 2809973
6469 Ntot 2508254
6470 Ntot 2973583
6471 Ntot 2622832
6472 Ntot 2828322
6473 Ntot 3036417
6474 Ntot 2612052
6475 Ntot 2842712
6476 Ntot 2723267
6477 Ntot 2650888
6478 Ntot 2893756
6479 Ntot 2623125
6480 Ntot 2674972
6481 Ntot 2766048
6482 Ntot 2646323
6483 Ntot 2676436
6484 Ntot 2698665
6485 Ntot 2932562
6486 Ntot 2844258
6487 Ntot 2640573
6488 Ntot 2654434
6489 Ntot 2698554
6490 Ntot 2686706
6491 Ntot 2883820
6492 Ntot 2745980
6493 Ntot 2816821
6494 Ntot 2719470
6495 Ntot 2751767
6496 Ntot 2959126
6497 Ntot 2810448
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11952 Ntot 2743687
11953 Ntot 2729568
11954 Ntot 2526442
11955 Ntot 2803267
11956 Ntot 2941485
11957 Ntot 2782682
11958 Ntot 2803189
11959 Ntot 2735219
11960 Ntot 2668482
11961 Ntot 2805678
11962 Ntot 2707818
11963 Ntot 2758027
11964 Ntot 2959266
11965 Ntot 2897986
11966 Ntot 2909612
11967 Ntot 2705795
11968 Ntot 2754847
11969 Ntot 2819988
11970 Ntot 2575291
11971 Ntot 2818411
11972 Ntot 2704570
11973 Ntot 2603382
11974 Ntot 2827374
11975 Ntot 2807947
11976 Ntot 2734898
11977 Ntot 2814612
11978 Ntot 2970324
11979 Ntot 2656016
11980 Ntot 2698417
11981 Ntot 2961252
11982 Ntot 2828531
11983 Ntot 2829407
11984 Ntot 2620575
11985 Ntot 2662359
11986 Ntot 2782299
11987 Ntot 2868178
11988 Ntot 2800392
11989 Ntot 2701948
11990 Ntot 2623542
11991 Ntot 2540921
11992 Ntot 2639099
11993 Ntot 2838583
11994 Ntot 2871694
11995 Ntot 2692769
11996 Ntot 2697434
11997 Ntot 2686570
11998 Ntot 2723863
11999 Ntot 2567039
12000 Ntot 2948012
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[1] "Value of parameter"
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[1] "Posterior plots with 95% credible intervals"
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[1] "density"
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[1] "quants"
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A plot of the \(logit(P)\) (the logit of the estimated probability of capture) is shown in ?@fig-btspas-diag1-logitP
$data
mean sd 2.5% 25% 50% 75%
logitP[1] -3.231698 0.13166827 -3.497633 -3.318289 -3.229264 -3.141008
logitP[2] -2.130373 0.08796830 -2.303911 -2.188610 -2.131085 -2.072361
logitP[3] -2.548131 0.23811194 -3.018273 -2.707732 -2.542864 -2.382758
logitP[4] -1.969197 0.08310100 -2.133044 -2.025039 -1.969582 -1.913775
logitP[5] -3.045225 0.11452159 -3.280643 -3.120658 -3.043189 -2.968012
logitP[6] -2.984068 0.14661543 -3.285655 -3.080481 -2.980426 -2.883478
logitP[7] -2.987145 0.17455309 -3.325219 -3.107043 -2.983866 -2.866972
logitP[8] -3.245073 0.05891636 -3.364442 -3.284550 -3.245334 -3.205374
logitP[9] -2.902177 0.05657181 -3.014050 -2.939995 -2.901456 -2.864548
logitP[10] -3.168038 0.08219533 -3.330144 -3.223521 -3.167514 -3.112814
logitP[11] -2.684641 0.05859884 -2.802081 -2.723134 -2.684892 -2.645085
logitP[12] -2.074265 0.05413162 -2.182144 -2.110587 -2.074178 -2.038139
logitP[13] -2.179161 0.09858649 -2.374061 -2.244765 -2.179621 -2.111672
logitP[14] -2.116590 0.16351244 -2.440340 -2.225951 -2.112243 -2.004697
logitP[15] -2.147474 0.28629293 -2.716532 -2.335621 -2.143557 -1.955828
logitP[16] -2.750555 0.42629097 -3.595089 -3.025926 -2.733124 -2.467695
97.5% Rhat n.eff time.index time lcl ucl
logitP[1] -2.984970 1.000761 6000 1 4 -3.497633 -2.984970
logitP[2] -1.960295 1.001229 4200 2 5 -2.303911 -1.960295
logitP[3] -2.107626 1.001593 2400 3 6 -3.018273 -2.107626
logitP[4] -1.807444 1.000789 6000 4 7 -2.133044 -1.807444
logitP[5] -2.823893 1.000856 6000 5 8 -3.280643 -2.823893
logitP[6] -2.707897 1.000810 6000 6 9 -3.285655 -2.707897
logitP[7] -2.650606 1.000854 6000 7 10 -3.325219 -2.650606
logitP[8] -3.133552 1.000792 6000 8 11 -3.364442 -3.133552
logitP[9] -2.792491 1.001348 3300 9 12 -3.014050 -2.792491
logitP[10] -3.007150 1.001269 3800 10 13 -3.330144 -3.007150
logitP[11] -2.569459 1.001283 3700 11 14 -2.802081 -2.569459
logitP[12] -1.967395 1.001042 6000 12 15 -2.182144 -1.967395
logitP[13] -1.988892 1.000818 6000 13 16 -2.374061 -1.988892
logitP[14] -1.803157 1.001025 6000 14 17 -2.440340 -1.803157
logitP[15] -1.593993 1.001405 3000 15 18 -2.716532 -1.593993
logitP[16] -1.937867 1.000932 6000 16 19 -3.595089 -1.937867
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$labels$y
[1] "logit(p) + 95% credible interval"
$labels$x
[1] "Time\nHorizontal line is estimated beta.logitP[1] \nInner fence is c.i. on beta.logitP[1] \nOuter fence is 95% range on logit(p)"
$labels$title
[1] " \nPlot of logit(p[i]) with 95% credible intervals"
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[1] "lcl"
$labels$ymax
[1] "ucl"
$labels$yintercept
[1] "yintercept"
attr(,"class")
[1] "gg" "ggplot"
A summary of the posterior for each parameter is also available. The estimates of total abundance can be extracted and summarized in a similar fashion as in the other models:
BTSPAS.diag.est1 <- Petersen::LP_BTSPAS_est (BTSPAS.diag.fit1)
BTSPAS.diag.est1$summary N_hat_f N_hat_rn N_hat N_hat_SE N_hat_conf_level N_hat_conf_method
1 NA NA 2750764 104131.5 0.95 Posterior
N_hat_LCL N_hat_UCL p_model name_model cond.ll n.parms nobs
1 2557856 2965873 ~1 p: ~1 NA NA 154081
Or, all of the parameters can be extracted directly from the BTSPAS object as shown below for the total abundance and the total unmarked abundance.
BTSPAS.diag.fit1$fit$summary[
row.names(BTSPAS.diag.fit1$fit$summary) %in% c("Ntot","Utot"),] mean sd 2.5% 25% 50% 75% 97.5% Rhat n.eff
Ntot 2750764 104131.5 2557856 2679591 2748473 2817332 2965873 1.000899 6000
Utot 2715779 104131.5 2522871 2644606 2713488 2782347 2930888 1.000899 6000
This also includes the Rubin-Brooks-Gelman statistic (\(Rhat\)) on mixing of the chains and the effective sample size of the posterior (after accounting for autocorrelation).
The estimated total abundance from BTSPAS is 2,750,764 (SD 104,132 ) fish.
Samples from the posterior are also included in the sims.matrix, sims.array and sims.list elements of the BTSPAS results object.
It is always important to do model assessment before accepting the results from the model fit. Please check the vignettes of BTSPAS on details on how to interpret the goodness of fit, trace, and autocorrelation plots.
8.3.4.3 Dealing with problems in the data
The BTSPAS package is quite flexible when dealing with problems in the data. Please consult the vignettes with the BTSPAS package for many examples.
8.3.4.3.1 Missing data from some strata
In some cases, data is missing for some temporal strata. For example, river flows could be too high to use the fishwheels safely; crews are sick; data are lost; etc. In these cases, the spline is used to interpolate the run abundance over the missing data.
For example, we will delete data from temporal strata 5 and 8. The resulting summary data is:
xtabs( freq ~ fw1 + fw2,
data=data_btspas_diag3.aug[ data_btspas_diag3.aug$fw1 %in% temporal_strata[1:10] &
data_btspas_diag3.aug$fw2 %in% temporal_strata[1:10] ,],
exclude=NULL, na.action=na.pass) fw2
fw1 0 4 6 7 9 10 11 12 13 14
0 0 14587 1027 1945 1323 933 57549 14846 5291 9249
4 1414 51 0 0 0 0 0 0 0 0
6 180 0 17 0 0 0 0 0 0 0
7 1167 0 0 168 0 0 0 0 0 0
9 880 0 0 0 43 0 0 0 0 0
10 582 0 0 0 0 28 0 0 0 0
11 7672 0 0 0 0 0 297 0 0 0
12 5695 0 0 0 0 0 0 313 0 0
13 3619 0 0 0 0 0 0 0 151 0
14 4545 0 0 0 0 0 0 0 0 309
Notice that there is no data for temporal strata 5 or 8.
We can also get the summary statistics (\(n_1\), \(m_2\), and \(u_2\)) for this data (and notice the warning messages):
# compute n, m,u
nmu <- Petersen::cap_hist_to_n_m_u(data_btspas_diag3)Warning in Petersen::cap_hist_to_n_m_u(data_btspas_diag3): *** Caution... Missing value for n1 set to 0 ***
Warning in Petersen::cap_hist_to_n_m_u(data_btspas_diag3): *** Caution... Missing value for u2. These are not set to zero ***
temp <- data.frame(time=nmu$..ts, n1=nmu$n1, m2=nmu$m2, u2=nmu$u2)
temp time n1 m2 u2
1 4 1465 51 14587
2 5 0 0 NA
3 6 197 17 1027
4 7 1335 168 1945
5 8 0 0 NA
6 9 923 43 1323
7 10 610 28 933
8 11 7969 297 57549
9 12 6008 313 14846
10 13 3770 151 5291
11 14 4854 309 9249
12 15 3350 376 4615
13 16 1062 110 1433
14 17 346 40 446
15 18 88 12 120
16 19 20 1 23
Notice that in stratum 5 and 8, the number of releases (\(n_1\)) and recaptures (\(m_2\)) are set to 0 (no data present), but the \(u_2\) values are set to NA (missing) indicating that the number of unmarked fish recaptured is unknown because the trap was not running.
We fit the BTSPAS model in the same way as previously.
BTSPAS.diag.fit3 <- Petersen::LP_BTSPAS_fit_Diag(
data_btspas_diag3,
p_model=~1,
jump.after=10,
InitialSeed=234234
)which gives the model fit summary:
The fitted spline curve to the number of unmarked fish available in each recovery sample is shown in ?@fig-btspas-diag3-fit-plot
$data
time logUi logU logUlcl logUucl spline
1 4 12.927686 12.870748 12.628092 13.130223 12.141153
2 5 NA 11.099866 9.621431 12.729523 11.094507
3 6 9.338304 9.589931 9.170411 10.054614 10.479818
4 7 9.641816 9.671664 9.524568 9.822385 10.140268
5 8 NA 9.938060 8.546256 11.524391 9.935922
6 9 10.234017 10.196858 9.925155 10.488059 9.794381
7 10 9.888913 9.874493 9.552240 10.240214 9.660129
8 11 14.246881 14.242148 14.128670 14.351760 14.188454
9 12 12.557340 12.564021 12.458354 12.674500 13.028688
10 13 11.785432 11.788974 11.635265 11.950952 12.056103
11 14 11.883777 11.878763 11.773516 11.983797 11.190367
12 15 10.622351 10.629986 10.530459 10.729449 10.351151
13 16 9.528483 9.555053 9.375053 9.741904 9.461895
14 17 8.241189 8.335322 8.045083 8.636142 8.461110
15 18 6.730651 7.051943 6.568192 7.574096 7.291075
16 19 5.575949 5.881865 5.049610 6.769213 5.894073
$layers
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geom_point: na.rm = FALSE
stat_identity: na.rm = FALSE
position_identity
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geom_point: na.rm = FALSE
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geom_line: na.rm = FALSE, orientation = NA
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mapping: ymin = ~logUlcl, ymax = ~logUucl
geom_errorbar: na.rm = FALSE, orientation = NA, width = 0.1
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$labels
$labels$y
[1] "log(U[i]) + 95% credible interval"
$labels$x
[1] "Time Index\nOpen/closed circles - initial and final estimates"
$labels$title
[1] ""
$labels$subtitle
[1] "Fitted spline curve with 95% credible intervals for estimated log(U[i])"
$labels$ymin
[1] "logUlcl"
$labels$ymax
[1] "logUucl"
attr(,"class")
[1] "gg" "ggplot"
Notice that the curve was interpolated at temporal strata 5 and 8 (with a much larger uncertainty) compared to the other temporal strata.
A plot of the \(logit(P)\) (the logit of the estimated probability of capture) is shown in ?@fig-btspas-diag3-logitP
$data
mean sd 2.5% 25% 50% 75%
logitP[1] -3.244538 0.13257796 -3.513328 -3.333153 -3.242738 -3.152992
logitP[2] -2.645604 0.57862657 -3.835580 -2.994285 -2.641751 -2.288546
logitP[3] -2.578597 0.23985347 -3.069219 -2.735522 -2.573735 -2.416246
logitP[4] -1.966909 0.08287820 -2.129034 -2.022486 -1.966976 -1.910156
logitP[5] -2.628422 0.56780920 -3.752556 -2.984687 -2.623984 -2.273001
logitP[6] -2.960155 0.14656117 -3.256647 -3.055440 -2.959173 -2.859740
logitP[7] -2.986749 0.17994917 -3.358333 -3.102912 -2.980153 -2.862603
logitP[8] -3.243406 0.05945823 -3.358075 -3.284021 -3.243618 -3.203281
logitP[9] -2.905233 0.05765564 -3.020753 -2.943317 -2.904222 -2.865531
logitP[10] -3.173755 0.08196937 -3.338911 -3.228708 -3.172940 -3.117523
logitP[11] -2.680429 0.05724164 -2.792317 -2.718878 -2.680332 -2.641420
logitP[12] -2.074375 0.05474580 -2.181102 -2.110295 -2.073864 -2.038187
logitP[13] -2.180072 0.10023464 -2.376577 -2.246388 -2.179985 -2.112735
logitP[14] -2.120235 0.16157727 -2.441884 -2.230467 -2.118523 -2.009281
logitP[15] -2.151095 0.27732567 -2.702129 -2.338798 -2.147739 -1.961460
logitP[16] -2.705442 0.43357932 -3.594034 -2.984441 -2.699150 -2.422858
97.5% Rhat n.eff time.index time lcl ucl
logitP[1] -2.991323 1.001036 6000 1 4 -3.513328 -2.991323
logitP[2] -1.494495 1.001406 3000 2 5 -3.835580 -1.494495
logitP[3] -2.124042 1.000839 6000 3 6 -3.069219 -2.124042
logitP[4] -1.807890 1.000794 6000 4 7 -2.129034 -1.807890
logitP[5] -1.482596 1.000824 6000 5 8 -3.752556 -1.482596
logitP[6] -2.681456 1.001288 3700 6 9 -3.256647 -2.681456
logitP[7] -2.651714 1.001782 1900 7 10 -3.358333 -2.651714
logitP[8] -3.126269 1.000797 6000 8 11 -3.358075 -3.126269
logitP[9] -2.794718 1.000869 6000 9 12 -3.020753 -2.794718
logitP[10] -3.018281 1.001309 3600 10 13 -3.338911 -3.018281
logitP[11] -2.569376 1.000809 6000 11 14 -2.792317 -2.569376
logitP[12] -1.968878 1.002131 1400 12 15 -2.181102 -1.968878
logitP[13] -1.986442 1.000993 6000 13 16 -2.376577 -1.986442
logitP[14] -1.809054 1.000989 6000 14 17 -2.441884 -1.809054
logitP[15] -1.618367 1.001254 4000 15 18 -2.702129 -1.618367
logitP[16] -1.870031 1.000837 6000 16 19 -3.594034 -1.870031
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In those cases with no data, the capture-probability is estimated from the hierarchical model (at the mean of the model) with high uncertainty, but this not used to estimate \(U_2\) because \(u_2\) is missing.
A summary of the posterior for each parameter is also available. The estimates of total abundance can be extracted and summarized in a similar fashion as in the other models. The estimate is similar to the case where there was no missing data, but the uncertainty is larger.
BTSPAS.diag.est3 <- Petersen::LP_BTSPAS_est (BTSPAS.diag.fit3)
BTSPAS.diag.est3$summary N_hat_f N_hat_rn N_hat N_hat_SE N_hat_conf_level N_hat_conf_method
1 NA NA 2782845 295438.5 0.95 Posterior
N_hat_LCL N_hat_UCL p_model name_model cond.ll n.parms nobs
1 2544770 3107300 ~1 p: ~1 NA NA 145384
8.3.4.3.2 Fixing p’s
In some cases, the second trap is not running and so there are no recaptures of tagged fish and no captures of untagged fish. This usually ends up with 0’s for the total number of untagged fish captured in a temporal stratum, even though fish were released.
We need to set the p’s in these strata to 0 rather than letting BTSPAS impute a value based on the hierarchical model for the p’s.
This is done by passing the temporal stratum where the \(logit(p)\) should be fixed typically at \(logit(p)=-10\) which corresponds to \(p=\) 0.0000454.
For example, to fix the \(logit(p)\) for temporal stratum 12, the following code would be used:
BTSPAS.diag.fit2 <- Petersen::LP_BTSPAS_fit_Diag(
data_btspas_diag1,
p_model=~1,
jump.after=10,
logitP.fixed=12, logitP.fixed.values=-10,
InitialSeed=23943242
)8.3.4.3.3 Using covariates to model the p’s
BTSPAS also allows you to model the p’s with additional covariates, such a temperature, stream flow, etc. It is not possible to use covariates to model the total number of unmarked fish. A separate data frame must be created with the covariate value for each of the temporal strata at the second wheel.
Here is the data frame with the covariate data. There must be a line for every temporal stratum between the first and last stratum, even those where the traps were not running.
..ts2 logflow
2 4 6.564691
3 5 7.077220
4 6 6.884975
5 7 6.984033
6 8 7.923348
7 9 8.072650
8 10 7.817110
9 11 7.681441
10 12 7.607920
11 13 7.438067
12 14 6.391612
13 15 6.276237
14 16 6.464555
15 17 7.159880
16 18 6.559354
17 19 6.113682
A preliminary plot of the empirical logit
shows an approximate quadratic fit to \(log(flow)\), but the uncertainty in each week is enormous! (Figure 21)
The summary statistics are:
We can also get the summary statistics (\(n_1\), \(m_2\), and \(u_2\)) for this data:
time n1 m2 u2
1 4 1465 51 14587
2 5 1335 146 2854
3 6 197 17 1027
4 7 1335 168 1945
5 8 1653 72 2855
6 9 923 43 1323
7 10 610 28 933
8 11 7969 297 57549
9 12 6008 313 14846
10 13 3770 151 5291
11 14 4854 309 9249
12 15 3350 376 4615
13 16 1062 110 1433
14 17 346 40 446
15 18 88 12 120
16 19 20 1 23
There is no missing data.
We fit the model by modifying the formula for p_model and including the covariate data
BTSPAS.diag.fit4 <- Petersen::LP_BTSPAS_fit_Diag(
data_btspas_diag1,
p_model=~logflow+I(logflow^2), p_model_cov=p_cov,
jump.after=10,
InitialSeed=23943242
)Then the estimates can be extracted in the usual fashion:
BTSPAS.diag.est4 <- Petersen::LP_BTSPAS_est (BTSPAS.diag.fit4)
BTSPAS.diag.est4$summary N_hat_f N_hat_rn N_hat N_hat_SE N_hat_conf_level N_hat_conf_method
1 NA NA 2743295 103613.3 0.95 Posterior
N_hat_LCL N_hat_UCL p_model name_model
1 2549144 2957416 ~logflow + I(logflow^2) p: ~logflow + I(logflow^2)
cond.ll n.parms nobs
1 NA NA 154081
There is only a minor change in the estimate compared to not using a covariate (seen previously)
8.3.5 Non-diagonal case
In this case, the released fish are not recaptured in a single future temporal stratum, and recaptures takes place for a number of future strata. Here is an example of data collected under this protocol. Fish were tagged and released on the Conne River each day (denoted by the julian day of the year). The fish move upstream and are recaptured at an upstream trap (along with untagged fish).
data(data_btspas_nondiag1)
data_btspas_nondiag1[ grepl("^027", data_btspas_nondiag1$cap_hist) |
grepl("000..027", data_btspas_nondiag1$cap_hist),] cap_hist freq
5 027..000 224
20 000..027 1420
28 027..028 1
34 027..029 39
40 027..030 84
47 027..031 35
54 027..032 1
61 027..033 3
68 027..034 1
In temporal stratum 27, 388 fish were released at the first fishwheel, of which 1 were recaptured in the next temporal stratum at the second fishwheel, 39 were recaptured in the following temporal stratum at the second fishwheel etc, and 224 were never seen again. An additional 1420 unmarked fish were captured at the second fishwheel.
Recaptures of marked fish no longer take place along the “diagonal” that was seen in the previous example (only the first 10 strata are shown below):
fw2
fw1 0 23 24 25 26 27 28 29 30 31 32 33
0 0 0 0 0 0 1420 27886 9284 4357 11871 14896 9910
23 21 0 0 0 0 0 11 2 0 0 0 0
24 132 0 0 0 0 3 118 18 6 3 0 0
25 328 0 0 0 0 1 149 76 33 16 3 1
26 294 0 0 0 0 0 42 163 69 34 1 0
27 224 0 0 0 0 0 1 39 84 35 1 3
28 100 0 0 0 0 0 0 1 29 60 14 5
29 266 0 0 0 0 0 0 0 3 82 84 19
30 291 0 0 0 0 0 0 0 0 20 154 56
31 191 0 0 0 0 0 0 0 0 0 16 44
The first row (corresponding to fw1=0) are the number of unmarked fish recovered at the second fish wheel in the temporal strata. The first column (corresponding to fw2=0) are the number of released marked fish that were never seen again.
Most fish seem to take between 4 to 10 weeks to move between fish wheels.
Note that the second fishwheel was not operating in temporal strata 23 to 26, so no recoveries are possible, and the number of unmarked fish recaptured is also 0. The capture probability will have to be set to 0 for these temporal strata.
The summary statistics are:
# compute n, m,u
nmu <- Petersen::cap_hist_to_n_m_u(data_btspas_nondiag1)
temp <- data.frame(time =nmu$..ts,
n1 =c(nmu$n1, rep(NA, length(nmu$u2)-length(nmu$n1))),
m2 =rbind(nmu$m2, matrix(NA, nrow=length(nmu$u2)-length(nmu$n1), ncol=ncol(nmu$m2))) ,
u2 =nmu$u2)
temp time n1 m2.1 m2.2 m2.3 m2.4 m2.5 m2.6 m2.7 m2.8 m2.9 m2.10 u2
1 23 34 0 0 0 0 0 11 2 0 0 0 0
2 24 280 0 0 0 3 118 18 6 3 0 0 0
3 25 607 0 0 1 149 76 33 16 3 1 0 0
4 26 603 0 0 42 163 69 34 1 0 0 0 0
5 27 388 0 1 39 84 35 1 3 1 0 0 1420
6 28 212 0 1 29 60 14 5 2 0 1 0 27886
7 29 468 0 3 82 84 19 11 2 1 0 0 9284
8 30 586 0 20 154 56 53 9 1 1 1 0 4357
9 31 512 0 16 44 146 83 25 3 3 0 1 11871
10 32 458 0 2 52 125 82 13 14 3 0 0 14896
11 33 479 0 0 83 133 43 12 5 2 0 0 9910
12 34 329 0 12 96 60 29 8 0 1 0 0 16526
13 35 248 0 19 72 37 17 7 0 0 0 0 17443
14 36 201 0 7 55 23 6 1 0 0 0 0 16485
15 37 104 0 7 3 3 0 0 0 0 0 0 6776
16 38 NA NA NA NA NA NA NA NA NA NA NA 4644
17 39 NA NA NA NA NA NA NA NA NA NA NA 2190
18 40 NA NA NA NA NA NA NA NA NA NA NA 1066
19 41 NA NA NA NA NA NA NA NA NA NA NA 166
8.3.5.1 Preliminary screening of the data
A pooled-Petersen estimator would add all of the marked, recaptured and unmarked fish to give an estimate of 283,200 (SE 3,616) fish but can the estimate be trusted?
Let us first examine a plot of the estimated capture efficiency at the second trap for each set of releases (Figure 22) formed by looking at the total number of recoveries / total fish released.
There are several unusual features
- There appears to be heterogeneity in the total capture probabilities across the season with a lower catchability early in the season and a higher catchability later in the season
- The fall off in catchability near the end of the season is a artefact of sampling ending while fish are still migrating.
Similarly, let us look at the pattern of unmarked fish captured at the second trap (Figure 23).
Again notice no untagged recoveries in weeks 23 to 26 and the large jump in recoveries.
8.3.5.2 Fitting the basic BTSPAS non-diagonal model
The Petersen package function BTSPAS_NonDiag_fit() is a wrapper to the corresponding function in the BTSPAS package that takes the (modified for bad events) data file, a model for the mean capture probabilities at the second temporal stratum (default is a common mean), and identification of break points in the underlying spline, and then call the function in the BTSPAS package, and formats the returned data structure to match the returning structure for other functions in this package.
If finer control over the fitting process is needed, the BTSPAS package should be called directly – please consult the vignettes that come with the BTSPAS package.
In this case, no sampling was done in weeks 23 to 27 and so we set the capture probability of 0 on these days:
BTSPAS.nondiag.fit1 <- LP_BTSPAS_fit_NonDiag(
data=data_btspas_nondiag1,
p_model=~1,
InitialSeed=34343,
logitP.fixed=c(23:26), logitP.fixed.values=rep(-10,length(23:26))
)The distribution of the posterior sample for the total number unmarked and total abundance is shown in ?@fig-btspas-diag1-postUN-nondiag
$data
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10 Utot 355432
11 Utot 321751
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13 Utot 342215
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25 Utot 312434
26 Utot 328223
27 Utot 295477
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390 Utot 301930
391 Utot 293291
392 Utot 346079
393 Utot 320373
394 Utot 342836
395 Utot 301502
396 Utot 287781
397 Utot 297225
398 Utot 356836
399 Utot 319261
400 Utot 302193
401 Utot 363903
402 Utot 300148
403 Utot 289831
404 Utot 326072
405 Utot 417734
406 Utot 402836
407 Utot 326952
408 Utot 308353
409 Utot 315924
410 Utot 309329
411 Utot 322994
412 Utot 296472
413 Utot 309758
414 Utot 316383
415 Utot 297382
416 Utot 365440
417 Utot 336819
418 Utot 289159
419 Utot 335299
420 Utot 419298
421 Utot 321590
422 Utot 348984
423 Utot 279434
424 Utot 277101
425 Utot 308477
426 Utot 355080
427 Utot 300958
428 Utot 330363
429 Utot 312983
430 Utot 434493
431 Utot 286962
432 Utot 358662
433 Utot 327596
434 Utot 346820
435 Utot 313802
436 Utot 301431
437 Utot 360072
438 Utot 365611
439 Utot 338155
440 Utot 368526
441 Utot 340315
442 Utot 334797
443 Utot 333438
444 Utot 321177
445 Utot 298079
446 Utot 312539
447 Utot 309117
448 Utot 384357
449 Utot 281671
450 Utot 376998
451 Utot 332907
452 Utot 310817
453 Utot 326403
454 Utot 328416
455 Utot 335372
456 Utot 304447
457 Utot 296532
458 Utot 324709
459 Utot 294977
460 Utot 388308
461 Utot 332641
462 Utot 272856
463 Utot 283303
464 Utot 332599
465 Utot 367609
466 Utot 321384
467 Utot 336678
468 Utot 386199
469 Utot 340905
470 Utot 301254
471 Utot 330404
472 Utot 322051
473 Utot 345762
474 Utot 389315
475 Utot 308862
476 Utot 309747
477 Utot 290952
478 Utot 395840
479 Utot 349867
480 Utot 323517
481 Utot 273214
482 Utot 350986
483 Utot 300220
484 Utot 327333
485 Utot 281788
486 Utot 316123
487 Utot 410109
488 Utot 330726
489 Utot 328329
490 Utot 412562
491 Utot 359848
492 Utot 359903
493 Utot 343698
494 Utot 319356
495 Utot 375255
496 Utot 288387
497 Utot 341241
498 Utot 351763
499 Utot 355588
500 Utot 310146
501 Utot 353058
502 Utot 311767
503 Utot 406724
504 Utot 296380
505 Utot 308532
506 Utot 317707
507 Utot 322023
508 Utot 330124
509 Utot 357901
510 Utot 351824
511 Utot 317363
512 Utot 331055
513 Utot 305102
514 Utot 346408
515 Utot 320887
516 Utot 343254
517 Utot 277220
518 Utot 284342
519 Utot 334268
520 Utot 319478
521 Utot 369290
522 Utot 336253
523 Utot 355476
524 Utot 366577
525 Utot 340087
526 Utot 301063
527 Utot 292817
528 Utot 301247
529 Utot 309092
530 Utot 344435
531 Utot 288858
532 Utot 412467
533 Utot 386057
534 Utot 331718
535 Utot 311718
536 Utot 317622
537 Utot 286507
538 Utot 355058
539 Utot 332501
540 Utot 322781
541 Utot 346277
542 Utot 331242
543 Utot 283405
544 Utot 312409
545 Utot 345333
546 Utot 329566
547 Utot 278062
548 Utot 308659
549 Utot 327816
550 Utot 478385
551 Utot 356698
552 Utot 304016
553 Utot 314554
554 Utot 327666
555 Utot 339120
556 Utot 361734
557 Utot 296510
558 Utot 308784
559 Utot 332201
560 Utot 334087
561 Utot 372551
562 Utot 352314
563 Utot 348280
564 Utot 296419
565 Utot 323765
566 Utot 300286
567 Utot 376279
568 Utot 359143
569 Utot 301410
570 Utot 268970
571 Utot 307975
572 Utot 324414
573 Utot 357009
574 Utot 358840
575 Utot 346616
576 Utot 291020
577 Utot 333903
578 Utot 298911
579 Utot 350791
580 Utot 321036
581 Utot 280219
582 Utot 347972
583 Utot 336967
584 Utot 294584
585 Utot 340077
586 Utot 346370
587 Utot 374251
588 Utot 289896
589 Utot 316328
590 Utot 298875
591 Utot 290544
592 Utot 312877
593 Utot 292344
594 Utot 308856
595 Utot 317226
596 Utot 348636
597 Utot 317422
598 Utot 381905
599 Utot 330575
600 Utot 359053
601 Utot 317504
602 Utot 309413
603 Utot 353208
604 Utot 368936
605 Utot 294171
606 Utot 344452
607 Utot 301932
608 Utot 324542
609 Utot 307380
610 Utot 332291
611 Utot 369443
612 Utot 351818
613 Utot 350743
614 Utot 302107
615 Utot 303901
616 Utot 367738
617 Utot 321478
618 Utot 287397
619 Utot 330758
620 Utot 315806
621 Utot 353741
622 Utot 374146
623 Utot 290200
624 Utot 357813
625 Utot 302362
626 Utot 342482
627 Utot 360121
628 Utot 331310
629 Utot 349712
630 Utot 293376
631 Utot 351261
632 Utot 318108
633 Utot 351334
634 Utot 348021
635 Utot 306435
636 Utot 352747
637 Utot 329444
638 Utot 332616
639 Utot 316560
640 Utot 302819
641 Utot 316976
642 Utot 325826
643 Utot 305788
644 Utot 306224
645 Utot 305516
646 Utot 303459
647 Utot 320408
648 Utot 396977
649 Utot 350484
650 Utot 306591
651 Utot 296920
652 Utot 313845
653 Utot 392883
654 Utot 318499
655 Utot 374068
656 Utot 304303
657 Utot 335556
658 Utot 358500
659 Utot 439522
660 Utot 340855
661 Utot 407713
662 Utot 298447
663 Utot 284169
664 Utot 316530
665 Utot 296335
666 Utot 317497
667 Utot 326967
668 Utot 346862
669 Utot 302557
670 Utot 346984
671 Utot 350372
672 Utot 346225
673 Utot 288313
674 Utot 349212
675 Utot 268323
676 Utot 397774
677 Utot 316244
678 Utot 356290
679 Utot 339085
680 Utot 305708
681 Utot 348557
682 Utot 313633
683 Utot 316772
684 Utot 346896
685 Utot 382229
686 Utot 300526
687 Utot 329707
688 Utot 295608
689 Utot 282500
690 Utot 323761
691 Utot 337541
692 Utot 319268
693 Utot 344590
694 Utot 285643
695 Utot 298314
696 Utot 288080
697 Utot 332757
698 Utot 288913
699 Utot 304213
700 Utot 324350
701 Utot 395416
702 Utot 313116
703 Utot 310592
704 Utot 361903
705 Utot 295822
706 Utot 301091
707 Utot 386929
708 Utot 302717
709 Utot 385252
710 Utot 368396
711 Utot 319329
712 Utot 288957
713 Utot 316061
714 Utot 282140
715 Utot 312006
716 Utot 312863
717 Utot 368392
718 Utot 376642
719 Utot 314810
720 Utot 267306
721 Utot 358626
722 Utot 391797
723 Utot 328608
724 Utot 304538
725 Utot 318226
726 Utot 307119
727 Utot 324527
728 Utot 381265
729 Utot 302549
730 Utot 329077
731 Utot 276297
732 Utot 344700
733 Utot 436618
734 Utot 413946
735 Utot 314736
736 Utot 374029
737 Utot 313027
738 Utot 320542
739 Utot 327793
740 Utot 329862
741 Utot 346919
742 Utot 391360
743 Utot 320916
744 Utot 316157
745 Utot 341447
746 Utot 297918
747 Utot 299106
748 Utot 362888
749 Utot 348369
750 Utot 334634
751 Utot 275615
752 Utot 303231
753 Utot 342058
754 Utot 297046
755 Utot 326970
756 Utot 316628
757 Utot 356975
758 Utot 389785
759 Utot 307242
760 Utot 374651
761 Utot 352947
762 Utot 335670
763 Utot 330937
764 Utot 384688
765 Utot 337826
766 Utot 343369
767 Utot 381799
768 Utot 308185
769 Utot 389301
770 Utot 332925
771 Utot 400250
772 Utot 331320
773 Utot 284694
774 Utot 307295
775 Utot 346327
776 Utot 331561
777 Utot 404480
778 Utot 305252
779 Utot 337568
780 Utot 340176
781 Utot 390684
782 Utot 302801
783 Utot 408926
784 Utot 333643
785 Utot 314701
786 Utot 305385
787 Utot 379287
788 Utot 295715
789 Utot 358187
790 Utot 355153
791 Utot 327375
792 Utot 338678
793 Utot 340173
794 Utot 319378
795 Utot 282946
796 Utot 304750
797 Utot 281436
798 Utot 293768
799 Utot 339336
800 Utot 322584
801 Utot 327417
802 Utot 331553
803 Utot 375631
804 Utot 305257
805 Utot 339696
806 Utot 314122
807 Utot 299194
808 Utot 303548
809 Utot 311253
810 Utot 319962
811 Utot 272025
812 Utot 292409
813 Utot 286334
814 Utot 311218
815 Utot 309629
816 Utot 358824
817 Utot 337441
818 Utot 332652
819 Utot 347252
820 Utot 389995
821 Utot 320841
822 Utot 403404
823 Utot 342892
824 Utot 318548
825 Utot 296166
826 Utot 312460
827 Utot 329602
828 Utot 347960
829 Utot 380998
830 Utot 350134
831 Utot 276547
832 Utot 304621
833 Utot 361416
834 Utot 318311
835 Utot 333640
836 Utot 354044
837 Utot 313063
838 Utot 309742
839 Utot 317871
840 Utot 335704
841 Utot 407012
842 Utot 307932
843 Utot 353616
844 Utot 365689
845 Utot 296679
846 Utot 406365
847 Utot 341621
848 Utot 291676
849 Utot 355913
850 Utot 314778
851 Utot 316927
852 Utot 307418
853 Utot 336977
854 Utot 290032
855 Utot 361159
856 Utot 315604
857 Utot 342099
858 Utot 332917
859 Utot 325615
860 Utot 298991
861 Utot 355009
862 Utot 375356
863 Utot 280373
864 Utot 413801
865 Utot 283217
866 Utot 309889
867 Utot 438801
868 Utot 297801
869 Utot 318330
870 Utot 312886
871 Utot 423872
872 Utot 329678
873 Utot 380280
874 Utot 307724
875 Utot 342685
876 Utot 320868
877 Utot 360337
878 Utot 297750
879 Utot 353702
880 Utot 340989
881 Utot 402729
882 Utot 361005
883 Utot 371746
884 Utot 321632
885 Utot 309033
886 Utot 304891
887 Utot 348370
888 Utot 343873
889 Utot 291116
890 Utot 331914
891 Utot 324543
892 Utot 287045
893 Utot 319954
894 Utot 311521
895 Utot 345593
896 Utot 346595
897 Utot 441005
898 Utot 339302
899 Utot 310320
900 Utot 319108
901 Utot 316563
902 Utot 322936
903 Utot 337184
904 Utot 389775
905 Utot 289126
906 Utot 371411
907 Utot 339998
908 Utot 318017
909 Utot 342114
910 Utot 310236
911 Utot 345645
912 Utot 345826
913 Utot 353216
914 Utot 321934
915 Utot 308125
916 Utot 362231
917 Utot 421541
918 Utot 364283
919 Utot 423485
920 Utot 338597
921 Utot 312956
922 Utot 303811
923 Utot 358251
924 Utot 317162
925 Utot 327833
926 Utot 330354
927 Utot 351691
928 Utot 302366
929 Utot 335155
930 Utot 349374
931 Utot 344781
932 Utot 366383
933 Utot 329840
934 Utot 398481
935 Utot 323408
936 Utot 375116
937 Utot 339559
938 Utot 322691
939 Utot 363537
940 Utot 335296
941 Utot 325539
942 Utot 292415
943 Utot 317486
944 Utot 330606
945 Utot 314060
946 Utot 344286
947 Utot 313256
948 Utot 333239
949 Utot 304178
950 Utot 358103
951 Utot 343999
952 Utot 282542
953 Utot 297722
954 Utot 339005
955 Utot 356022
956 Utot 313702
957 Utot 303457
958 Utot 318027
959 Utot 373734
960 Utot 373391
961 Utot 328561
962 Utot 317117
963 Utot 291596
964 Utot 310625
965 Utot 312804
966 Utot 315456
967 Utot 350458
968 Utot 326698
969 Utot 308886
970 Utot 287633
971 Utot 327122
972 Utot 316454
973 Utot 292689
974 Utot 308165
975 Utot 357636
976 Utot 310488
977 Utot 324594
978 Utot 285053
979 Utot 330403
980 Utot 325085
981 Utot 322574
982 Utot 330550
983 Utot 450020
984 Utot 365481
985 Utot 355298
986 Utot 295246
987 Utot 308169
988 Utot 331011
989 Utot 355751
990 Utot 381367
991 Utot 312589
992 Utot 374008
993 Utot 348287
994 Utot 334115
995 Utot 317078
996 Utot 324782
997 Utot 309373
998 Utot 288188
999 Utot 355262
1000 Utot 303189
1001 Utot 344214
1002 Utot 288603
1003 Utot 310712
1004 Utot 359820
1005 Utot 346036
1006 Utot 369838
1007 Utot 292026
1008 Utot 395675
1009 Utot 349911
1010 Utot 341689
1011 Utot 359956
1012 Utot 304653
1013 Utot 323592
1014 Utot 328898
1015 Utot 303955
1016 Utot 324288
1017 Utot 298564
1018 Utot 329259
1019 Utot 330137
1020 Utot 319125
1021 Utot 312494
1022 Utot 378053
1023 Utot 319384
1024 Utot 351258
1025 Utot 359608
1026 Utot 296663
1027 Utot 376865
1028 Utot 281571
1029 Utot 352237
1030 Utot 293784
1031 Utot 290060
1032 Utot 366945
1033 Utot 330976
1034 Utot 274448
1035 Utot 364905
1036 Utot 359193
1037 Utot 365159
1038 Utot 345160
1039 Utot 343257
1040 Utot 386009
1041 Utot 399160
1042 Utot 316133
1043 Utot 318830
1044 Utot 287560
1045 Utot 365334
1046 Utot 372966
1047 Utot 283353
1048 Utot 308042
1049 Utot 351382
1050 Utot 383890
1051 Utot 284786
1052 Utot 366086
1053 Utot 317944
1054 Utot 312339
1055 Utot 347034
1056 Utot 333968
1057 Utot 305539
1058 Utot 281262
1059 Utot 295508
1060 Utot 293647
1061 Utot 310809
1062 Utot 329921
1063 Utot 354288
1064 Utot 354294
1065 Utot 357179
1066 Utot 306242
1067 Utot 310318
1068 Utot 330716
1069 Utot 378025
1070 Utot 325001
1071 Utot 328759
1072 Utot 384693
1073 Utot 388725
1074 Utot 311880
1075 Utot 304335
1076 Utot 332389
1077 Utot 326693
1078 Utot 301551
1079 Utot 330699
1080 Utot 359041
1081 Utot 408574
1082 Utot 374628
1083 Utot 313828
1084 Utot 357380
1085 Utot 305732
1086 Utot 300781
1087 Utot 298975
1088 Utot 353301
1089 Utot 335300
1090 Utot 313248
1091 Utot 310172
1092 Utot 326928
1093 Utot 369095
1094 Utot 353247
1095 Utot 410266
1096 Utot 356659
1097 Utot 339229
1098 Utot 374166
1099 Utot 287351
1100 Utot 313760
1101 Utot 286878
1102 Utot 340339
1103 Utot 304952
1104 Utot 280010
1105 Utot 276973
1106 Utot 311202
1107 Utot 323859
1108 Utot 292500
1109 Utot 308262
1110 Utot 336740
1111 Utot 364521
1112 Utot 329898
1113 Utot 336818
1114 Utot 272018
1115 Utot 317798
1116 Utot 341178
1117 Utot 327541
1118 Utot 428821
1119 Utot 357067
1120 Utot 299433
1121 Utot 288476
1122 Utot 334601
1123 Utot 368007
1124 Utot 316873
1125 Utot 286693
1126 Utot 332312
1127 Utot 383679
1128 Utot 358093
1129 Utot 293872
1130 Utot 327213
1131 Utot 341256
1132 Utot 308660
1133 Utot 292111
1134 Utot 375122
1135 Utot 285821
1136 Utot 371876
1137 Utot 327555
1138 Utot 300531
1139 Utot 290157
1140 Utot 310251
1141 Utot 332841
1142 Utot 401595
1143 Utot 327019
1144 Utot 313082
1145 Utot 302456
1146 Utot 402486
1147 Utot 314192
1148 Utot 346051
1149 Utot 300985
1150 Utot 305564
1151 Utot 382319
1152 Utot 302498
1153 Utot 328232
1154 Utot 293504
1155 Utot 297124
1156 Utot 327040
1157 Utot 311573
1158 Utot 328839
1159 Utot 340445
1160 Utot 368068
1161 Utot 390384
1162 Utot 339089
1163 Utot 335376
1164 Utot 307982
1165 Utot 351805
1166 Utot 337692
1167 Utot 312558
1168 Utot 365652
1169 Utot 340805
1170 Utot 306024
1171 Utot 277383
1172 Utot 342600
1173 Utot 294543
1174 Utot 334977
1175 Utot 317448
1176 Utot 300516
1177 Utot 292242
1178 Utot 326625
1179 Utot 346140
1180 Utot 340289
1181 Utot 351679
1182 Utot 366979
1183 Utot 314232
1184 Utot 303626
1185 Utot 402030
1186 Utot 321006
1187 Utot 331874
1188 Utot 261914
1189 Utot 340200
1190 Utot 322221
1191 Utot 336858
1192 Utot 321867
1193 Utot 289619
1194 Utot 296842
1195 Utot 309249
1196 Utot 342002
1197 Utot 422342
1198 Utot 311751
1199 Utot 333512
1200 Utot 340480
1201 Utot 378825
1202 Utot 357409
1203 Utot 387852
1204 Utot 332794
1205 Utot 302508
1206 Utot 337457
1207 Utot 348632
1208 Utot 345693
1209 Utot 344636
1210 Utot 288853
1211 Utot 317508
1212 Utot 321369
1213 Utot 314156
1214 Utot 323102
1215 Utot 329243
1216 Utot 292007
1217 Utot 335587
1218 Utot 295193
1219 Utot 376391
1220 Utot 324945
1221 Utot 272792
1222 Utot 319061
1223 Utot 349202
1224 Utot 353244
1225 Utot 385545
1226 Utot 311909
1227 Utot 330150
1228 Utot 345927
1229 Utot 313221
1230 Utot 283741
1231 Utot 340964
1232 Utot 308455
1233 Utot 296630
1234 Utot 348779
1235 Utot 326952
1236 Utot 296253
1237 Utot 281506
1238 Utot 377298
1239 Utot 323743
1240 Utot 342067
1241 Utot 285007
1242 Utot 306312
1243 Utot 347643
1244 Utot 352307
1245 Utot 420802
1246 Utot 372391
1247 Utot 332411
1248 Utot 348033
1249 Utot 324207
1250 Utot 322504
1251 Utot 316863
1252 Utot 360825
1253 Utot 305868
1254 Utot 347475
1255 Utot 283129
1256 Utot 377930
1257 Utot 328168
1258 Utot 289827
1259 Utot 321609
1260 Utot 358398
1261 Utot 338928
1262 Utot 372177
1263 Utot 331329
1264 Utot 302064
1265 Utot 284270
1266 Utot 294399
1267 Utot 280731
1268 Utot 298408
1269 Utot 366320
1270 Utot 268875
1271 Utot 391320
1272 Utot 303269
1273 Utot 303694
1274 Utot 300323
1275 Utot 353074
1276 Utot 367608
1277 Utot 289388
1278 Utot 372355
1279 Utot 292984
1280 Utot 327560
1281 Utot 319884
1282 Utot 315832
1283 Utot 286306
1284 Utot 304699
1285 Utot 389496
1286 Utot 345807
1287 Utot 312583
1288 Utot 299951
1289 Utot 312605
1290 Utot 330148
1291 Utot 320557
1292 Utot 292258
1293 Utot 353678
1294 Utot 342809
1295 Utot 328482
1296 Utot 375509
1297 Utot 319614
1298 Utot 326464
1299 Utot 368742
1300 Utot 329384
1301 Utot 409390
1302 Utot 317039
1303 Utot 305185
1304 Utot 353565
1305 Utot 372648
1306 Utot 310426
1307 Utot 341656
1308 Utot 295240
1309 Utot 340207
1310 Utot 342220
1311 Utot 292510
1312 Utot 295277
1313 Utot 342768
1314 Utot 325911
1315 Utot 367367
1316 Utot 335312
1317 Utot 329638
1318 Utot 330782
1319 Utot 301586
1320 Utot 389732
1321 Utot 306081
1322 Utot 319051
1323 Utot 311339
1324 Utot 385351
1325 Utot 330868
1326 Utot 327116
1327 Utot 309750
1328 Utot 368080
1329 Utot 313707
1330 Utot 317811
1331 Utot 392539
1332 Utot 350969
1333 Utot 330210
1334 Utot 315486
1335 Utot 342236
1336 Utot 340475
1337 Utot 333332
1338 Utot 313591
1339 Utot 305501
1340 Utot 350915
1341 Utot 392792
1342 Utot 296440
1343 Utot 308345
1344 Utot 274971
1345 Utot 292645
1346 Utot 369564
1347 Utot 339308
1348 Utot 375671
1349 Utot 367585
1350 Utot 343790
1351 Utot 327141
1352 Utot 321587
1353 Utot 368021
1354 Utot 344058
1355 Utot 296360
1356 Utot 396497
1357 Utot 401412
1358 Utot 342123
1359 Utot 292450
1360 Utot 348835
1361 Utot 310608
1362 Utot 316448
1363 Utot 313718
1364 Utot 305776
1365 Utot 325232
1366 Utot 310827
1367 Utot 287567
1368 Utot 293422
1369 Utot 301816
1370 Utot 326750
1371 Utot 308386
1372 Utot 332468
1373 Utot 266474
1374 Utot 381979
1375 Utot 374316
1376 Utot 302811
1377 Utot 362264
1378 Utot 378318
1379 Utot 311800
1380 Utot 374565
1381 Utot 347341
1382 Utot 301608
1383 Utot 320164
1384 Utot 386993
1385 Utot 323326
1386 Utot 362520
1387 Utot 380839
1388 Utot 318965
1389 Utot 381866
1390 Utot 392334
1391 Utot 407093
1392 Utot 324045
1393 Utot 322854
1394 Utot 319427
1395 Utot 382835
1396 Utot 302393
1397 Utot 361537
1398 Utot 316304
1399 Utot 351636
1400 Utot 298040
1401 Utot 311439
1402 Utot 450002
1403 Utot 296231
1404 Utot 355134
1405 Utot 355314
1406 Utot 302423
1407 Utot 297124
1408 Utot 322926
1409 Utot 300501
1410 Utot 317627
1411 Utot 295934
1412 Utot 341557
1413 Utot 331871
1414 Utot 356634
1415 Utot 342822
1416 Utot 338444
1417 Utot 310188
1418 Utot 282479
1419 Utot 346899
1420 Utot 316506
1421 Utot 314806
1422 Utot 386738
1423 Utot 332971
1424 Utot 324480
1425 Utot 377631
1426 Utot 299973
1427 Utot 336214
1428 Utot 296754
1429 Utot 298020
1430 Utot 311261
1431 Utot 292703
1432 Utot 316612
1433 Utot 316238
1434 Utot 407698
1435 Utot 292007
1436 Utot 337748
1437 Utot 338169
1438 Utot 411234
1439 Utot 313362
1440 Utot 277418
1441 Utot 323152
1442 Utot 418436
1443 Utot 338097
1444 Utot 346402
1445 Utot 291973
1446 Utot 327544
1447 Utot 349378
1448 Utot 324534
1449 Utot 455838
1450 Utot 351181
1451 Utot 325766
1452 Utot 372442
1453 Utot 322789
1454 Utot 302421
1455 Utot 350797
1456 Utot 364296
1457 Utot 298006
1458 Utot 353001
1459 Utot 284583
1460 Utot 303903
1461 Utot 332403
1462 Utot 322911
1463 Utot 314473
1464 Utot 323077
1465 Utot 299811
1466 Utot 331575
1467 Utot 350386
1468 Utot 309355
1469 Utot 375935
1470 Utot 419841
1471 Utot 333809
1472 Utot 300244
1473 Utot 360650
1474 Utot 355879
1475 Utot 313857
1476 Utot 361778
1477 Utot 305390
1478 Utot 313072
1479 Utot 319252
1480 Utot 340615
1481 Utot 301682
1482 Utot 291514
1483 Utot 407965
1484 Utot 308117
1485 Utot 327734
1486 Utot 318921
1487 Utot 322614
1488 Utot 325440
1489 Utot 293783
1490 Utot 307528
1491 Utot 410489
1492 Utot 321358
1493 Utot 288514
1494 Utot 303779
1495 Utot 440378
1496 Utot 300994
1497 Utot 418082
1498 Utot 290250
1499 Utot 348772
1500 Utot 353618
1501 Utot 299825
1502 Utot 402598
1503 Utot 342403
1504 Utot 327624
1505 Utot 297252
1506 Utot 333718
1507 Utot 340920
1508 Utot 339032
1509 Utot 335963
1510 Utot 301437
1511 Utot 323808
1512 Utot 377417
1513 Utot 407292
1514 Utot 348283
1515 Utot 322853
1516 Utot 299927
1517 Utot 266895
1518 Utot 352206
1519 Utot 333913
1520 Utot 304258
1521 Utot 302009
1522 Utot 320429
1523 Utot 288768
1524 Utot 357220
1525 Utot 307966
1526 Utot 301885
1527 Utot 373083
1528 Utot 310271
1529 Utot 366419
1530 Utot 332195
1531 Utot 366642
1532 Utot 374837
1533 Utot 292613
1534 Utot 302419
1535 Utot 371274
1536 Utot 317047
1537 Utot 305315
1538 Utot 367416
1539 Utot 295675
1540 Utot 323022
1541 Utot 336898
1542 Utot 283288
1543 Utot 355455
1544 Utot 341477
1545 Utot 329934
1546 Utot 292587
1547 Utot 340386
1548 Utot 290456
1549 Utot 391523
1550 Utot 372479
1551 Utot 364877
1552 Utot 279062
1553 Utot 314971
1554 Utot 314447
1555 Utot 333083
1556 Utot 326265
1557 Utot 292279
1558 Utot 320376
1559 Utot 415394
1560 Utot 314695
1561 Utot 330889
1562 Utot 297403
1563 Utot 330500
1564 Utot 323925
1565 Utot 327422
1566 Utot 345530
1567 Utot 357440
1568 Utot 371769
1569 Utot 430443
1570 Utot 323790
1571 Utot 320225
1572 Utot 305904
1573 Utot 310537
1574 Utot 331431
1575 Utot 323918
1576 Utot 301749
1577 Utot 293506
1578 Utot 430766
1579 Utot 282495
1580 Utot 264637
1581 Utot 366528
1582 Utot 365226
1583 Utot 363083
1584 Utot 332901
1585 Utot 299070
1586 Utot 329639
1587 Utot 299343
1588 Utot 320110
1589 Utot 309847
1590 Utot 398976
1591 Utot 354238
1592 Utot 290964
1593 Utot 331841
1594 Utot 316735
1595 Utot 328232
1596 Utot 329118
1597 Utot 324217
1598 Utot 297090
1599 Utot 327696
1600 Utot 378867
1601 Utot 298357
1602 Utot 334609
1603 Utot 323733
1604 Utot 322359
1605 Utot 349110
1606 Utot 307067
1607 Utot 334342
1608 Utot 330975
1609 Utot 406463
1610 Utot 337936
1611 Utot 345582
1612 Utot 389417
1613 Utot 330691
1614 Utot 331694
1615 Utot 342299
1616 Utot 336172
1617 Utot 346056
1618 Utot 323321
1619 Utot 357539
1620 Utot 298529
1621 Utot 313687
1622 Utot 319782
1623 Utot 340091
1624 Utot 384843
1625 Utot 318903
1626 Utot 411067
1627 Utot 311875
1628 Utot 323677
1629 Utot 332846
1630 Utot 344094
1631 Utot 327224
1632 Utot 324898
1633 Utot 291426
1634 Utot 337719
1635 Utot 347398
1636 Utot 335005
1637 Utot 328396
1638 Utot 278783
1639 Utot 268003
1640 Utot 309351
1641 Utot 354807
1642 Utot 301436
1643 Utot 375096
1644 Utot 378733
1645 Utot 325016
1646 Utot 303327
1647 Utot 342848
1648 Utot 341430
1649 Utot 325368
1650 Utot 328610
1651 Utot 331699
1652 Utot 304197
1653 Utot 320978
1654 Utot 311424
1655 Utot 334783
1656 Utot 324217
1657 Utot 331344
1658 Utot 314509
1659 Utot 288590
1660 Utot 372900
1661 Utot 344777
1662 Utot 332842
1663 Utot 400942
1664 Utot 320171
1665 Utot 299133
1666 Utot 307128
1667 Utot 375790
1668 Utot 355009
1669 Utot 329351
1670 Utot 313354
1671 Utot 332719
1672 Utot 337277
1673 Utot 358679
1674 Utot 354985
1675 Utot 376716
1676 Utot 349743
1677 Utot 294449
1678 Utot 305366
1679 Utot 356874
1680 Utot 348145
1681 Utot 327103
1682 Utot 319597
1683 Utot 419983
1684 Utot 338534
1685 Utot 323237
1686 Utot 313938
1687 Utot 329002
1688 Utot 294572
1689 Utot 325898
1690 Utot 364488
1691 Utot 300276
1692 Utot 317175
1693 Utot 316406
1694 Utot 301934
1695 Utot 367284
1696 Utot 393470
1697 Utot 341451
1698 Utot 318835
1699 Utot 340804
1700 Utot 277092
1701 Utot 299403
1702 Utot 417917
1703 Utot 281547
1704 Utot 326280
1705 Utot 420786
1706 Utot 339845
1707 Utot 304439
1708 Utot 347800
1709 Utot 342240
1710 Utot 325664
1711 Utot 335009
1712 Utot 333167
1713 Utot 294499
1714 Utot 337917
1715 Utot 334350
1716 Utot 323001
1717 Utot 285075
1718 Utot 289087
1719 Utot 306716
1720 Utot 275228
1721 Utot 308569
1722 Utot 303262
1723 Utot 351330
1724 Utot 447922
1725 Utot 306706
1726 Utot 385049
1727 Utot 350497
1728 Utot 313867
1729 Utot 288348
1730 Utot 361246
1731 Utot 319817
1732 Utot 309598
1733 Utot 389079
1734 Utot 304663
1735 Utot 359632
1736 Utot 353315
1737 Utot 344876
1738 Utot 292444
1739 Utot 322099
1740 Utot 285141
1741 Utot 345855
1742 Utot 325372
1743 Utot 402988
1744 Utot 299909
1745 Utot 377279
1746 Utot 314292
1747 Utot 308788
1748 Utot 311603
1749 Utot 302073
1750 Utot 340130
1751 Utot 375988
1752 Utot 330798
1753 Utot 316774
1754 Utot 345692
1755 Utot 330244
1756 Utot 302934
1757 Utot 308743
1758 Utot 357639
1759 Utot 380509
1760 Utot 302357
1761 Utot 304404
1762 Utot 331952
1763 Utot 371708
1764 Utot 303042
1765 Utot 326193
1766 Utot 350743
1767 Utot 347600
1768 Utot 299077
1769 Utot 401869
1770 Utot 349639
1771 Utot 396412
1772 Utot 428775
1773 Utot 332302
1774 Utot 313828
1775 Utot 335910
1776 Utot 407867
1777 Utot 327166
1778 Utot 305360
1779 Utot 281533
1780 Utot 301704
1781 Utot 398094
1782 Utot 328198
1783 Utot 298381
1784 Utot 322103
1785 Utot 295385
1786 Utot 354454
1787 Utot 322662
1788 Utot 335550
1789 Utot 370793
1790 Utot 424372
1791 Utot 301436
1792 Utot 326901
1793 Utot 334768
1794 Utot 378615
1795 Utot 315496
1796 Utot 377388
1797 Utot 328814
1798 Utot 354673
1799 Utot 379266
1800 Utot 268008
1801 Utot 364953
1802 Utot 286644
1803 Utot 375988
1804 Utot 345916
1805 Utot 376961
1806 Utot 308952
1807 Utot 285995
1808 Utot 289460
1809 Utot 283948
1810 Utot 303479
1811 Utot 369373
1812 Utot 354133
1813 Utot 332102
1814 Utot 303272
1815 Utot 265817
1816 Utot 328761
1817 Utot 339406
1818 Utot 341342
1819 Utot 340927
1820 Utot 326886
1821 Utot 333542
1822 Utot 410802
1823 Utot 345599
1824 Utot 285119
1825 Utot 340514
1826 Utot 328752
1827 Utot 375371
1828 Utot 336022
1829 Utot 320706
1830 Utot 386126
1831 Utot 324332
1832 Utot 306838
1833 Utot 308409
1834 Utot 368354
1835 Utot 340923
1836 Utot 368883
1837 Utot 303314
1838 Utot 282133
1839 Utot 301043
1840 Utot 326282
1841 Utot 333954
1842 Utot 322538
1843 Utot 317929
1844 Utot 329718
1845 Utot 304789
1846 Utot 395210
1847 Utot 358597
1848 Utot 338512
1849 Utot 307226
1850 Utot 318770
1851 Utot 304809
1852 Utot 289856
1853 Utot 322346
1854 Utot 386240
1855 Utot 326256
1856 Utot 319726
1857 Utot 297741
1858 Utot 328490
1859 Utot 319223
1860 Utot 336804
1861 Utot 329180
1862 Utot 311957
1863 Utot 320011
1864 Utot 344672
1865 Utot 416517
1866 Utot 381115
1867 Utot 357071
1868 Utot 294784
1869 Utot 325817
1870 Utot 297993
1871 Utot 340681
1872 Utot 338282
1873 Utot 333401
1874 Utot 298318
1875 Utot 310803
1876 Utot 322562
1877 Utot 336796
1878 Utot 286164
1879 Utot 342490
1880 Utot 304594
1881 Utot 289171
1882 Utot 347817
1883 Utot 354177
1884 Utot 313424
1885 Utot 280593
1886 Utot 345050
1887 Utot 313380
1888 Utot 395242
1889 Utot 304410
1890 Utot 360237
1891 Utot 331298
1892 Utot 295810
1893 Utot 294068
1894 Utot 314459
1895 Utot 281285
1896 Utot 296429
1897 Utot 314726
1898 Utot 309265
1899 Utot 398376
1900 Utot 288261
1901 Utot 310609
1902 Utot 346128
1903 Utot 317845
1904 Utot 326823
1905 Utot 325610
1906 Utot 281760
1907 Utot 376010
1908 Utot 421897
1909 Utot 304094
1910 Utot 344502
1911 Utot 323726
1912 Utot 298569
1913 Utot 294596
1914 Utot 337761
1915 Utot 312760
1916 Utot 350442
1917 Utot 311548
1918 Utot 357827
1919 Utot 377342
1920 Utot 380234
1921 Utot 331125
1922 Utot 323710
1923 Utot 300888
1924 Utot 361589
1925 Utot 324555
1926 Utot 338065
1927 Utot 405246
1928 Utot 293167
1929 Utot 306376
1930 Utot 316331
1931 Utot 345321
1932 Utot 444443
1933 Utot 349290
1934 Utot 352774
1935 Utot 314372
1936 Utot 284970
1937 Utot 349490
1938 Utot 368897
1939 Utot 347219
1940 Utot 314740
1941 Utot 349303
1942 Utot 318496
1943 Utot 326897
1944 Utot 337677
1945 Utot 287286
1946 Utot 328394
1947 Utot 367170
1948 Utot 362925
1949 Utot 319190
1950 Utot 317675
1951 Utot 311425
1952 Utot 336930
1953 Utot 355754
1954 Utot 385481
1955 Utot 304853
1956 Utot 285425
1957 Utot 336938
1958 Utot 347372
1959 Utot 331895
1960 Utot 368240
1961 Utot 308980
1962 Utot 294982
1963 Utot 361256
1964 Utot 305256
1965 Utot 327059
1966 Utot 357737
1967 Utot 317075
1968 Utot 361952
1969 Utot 309105
1970 Utot 320291
1971 Utot 330163
1972 Utot 310917
1973 Utot 288812
1974 Utot 332003
1975 Utot 389847
1976 Utot 307349
1977 Utot 360492
1978 Utot 334866
1979 Utot 385825
1980 Utot 287870
1981 Utot 314420
1982 Utot 310086
1983 Utot 293530
1984 Utot 451158
1985 Utot 366631
1986 Utot 360841
1987 Utot 316028
1988 Utot 340885
1989 Utot 383552
1990 Utot 362258
1991 Utot 330413
1992 Utot 349890
1993 Utot 355428
1994 Utot 354100
1995 Utot 307728
1996 Utot 296775
1997 Utot 295638
1998 Utot 341428
1999 Utot 324284
2000 Utot 351005
2001 Utot 294420
2002 Utot 325751
2003 Utot 308685
2004 Utot 290557
2005 Utot 322287
2006 Utot 412734
2007 Utot 318294
2008 Utot 295829
2009 Utot 349822
2010 Utot 362434
2011 Utot 336616
2012 Utot 287269
2013 Utot 262982
2014 Utot 410416
2015 Utot 318096
2016 Utot 321735
2017 Utot 352529
2018 Utot 315389
2019 Utot 324806
2020 Utot 346394
2021 Utot 336366
2022 Utot 316312
2023 Utot 435356
2024 Utot 363733
2025 Utot 297616
2026 Utot 375089
2027 Utot 333691
2028 Utot 311757
2029 Utot 340812
2030 Utot 356787
2031 Utot 365011
2032 Utot 348390
2033 Utot 322265
2034 Utot 321330
2035 Utot 297165
2036 Utot 304464
2037 Utot 346016
2038 Utot 317051
2039 Utot 330126
2040 Utot 331823
2041 Utot 427434
2042 Utot 324863
2043 Utot 302062
2044 Utot 383465
2045 Utot 335796
2046 Utot 349114
2047 Utot 305163
2048 Utot 285481
2049 Utot 319155
2050 Utot 334870
2051 Utot 282957
2052 Utot 348048
2053 Utot 342654
2054 Utot 397012
2055 Utot 338783
2056 Utot 300701
2057 Utot 366377
2058 Utot 301019
2059 Utot 289427
2060 Utot 353527
2061 Utot 332737
2062 Utot 290286
2063 Utot 284602
2064 Utot 334492
2065 Utot 305532
2066 Utot 324454
2067 Utot 371376
2068 Utot 295702
2069 Utot 330844
2070 Utot 329676
2071 Utot 347487
2072 Utot 283232
2073 Utot 358594
2074 Utot 311681
2075 Utot 325267
2076 Utot 362472
2077 Utot 336867
2078 Utot 412271
2079 Utot 297927
2080 Utot 324761
2081 Utot 352605
2082 Utot 363537
2083 Utot 317577
2084 Utot 324173
2085 Utot 309408
2086 Utot 270461
2087 Utot 343790
2088 Utot 318199
2089 Utot 388219
2090 Utot 310889
2091 Utot 301392
2092 Utot 297220
2093 Utot 327117
2094 Utot 309968
2095 Utot 306747
2096 Utot 289779
2097 Utot 331903
2098 Utot 301612
2099 Utot 323991
2100 Utot 322527
2101 Utot 281677
2102 Utot 315020
2103 Utot 349203
2104 Utot 293258
2105 Utot 316291
2106 Utot 291648
2107 Utot 286557
2108 Utot 303153
2109 Utot 330279
2110 Utot 350883
2111 Utot 308447
2112 Utot 322159
2113 Utot 356556
2114 Utot 356280
2115 Utot 267718
2116 Utot 365398
2117 Utot 324683
2118 Utot 299301
2119 Utot 364866
2120 Utot 284872
2121 Utot 391736
2122 Utot 270565
2123 Utot 325811
2124 Utot 401569
2125 Utot 398442
2126 Utot 362101
2127 Utot 347118
2128 Utot 339151
2129 Utot 349494
2130 Utot 347499
2131 Utot 330426
2132 Utot 336434
2133 Utot 359231
2134 Utot 345149
2135 Utot 355479
2136 Utot 364134
2137 Utot 294542
2138 Utot 351760
2139 Utot 306244
2140 Utot 292018
2141 Utot 339757
2142 Utot 355073
2143 Utot 313267
2144 Utot 333690
2145 Utot 302867
2146 Utot 376844
2147 Utot 294281
2148 Utot 319964
2149 Utot 359526
2150 Utot 303707
2151 Utot 364674
2152 Utot 297594
2153 Utot 309286
2154 Utot 443768
2155 Utot 411724
2156 Utot 377676
2157 Utot 322818
2158 Utot 386149
2159 Utot 301994
2160 Utot 344932
2161 Utot 296548
2162 Utot 358665
2163 Utot 318283
2164 Utot 351384
2165 Utot 333774
2166 Utot 330779
2167 Utot 356637
2168 Utot 415738
2169 Utot 311901
2170 Utot 320664
2171 Utot 351961
2172 Utot 345239
2173 Utot 424395
2174 Utot 351898
2175 Utot 346992
2176 Utot 334582
2177 Utot 307559
2178 Utot 292325
2179 Utot 287728
2180 Utot 293255
2181 Utot 286243
2182 Utot 282124
2183 Utot 297374
2184 Utot 371307
2185 Utot 382775
2186 Utot 312564
2187 Utot 308671
2188 Utot 313091
2189 Utot 294857
2190 Utot 312519
2191 Utot 342100
2192 Utot 359000
2193 Utot 379073
2194 Utot 332450
2195 Utot 320717
2196 Utot 307017
2197 Utot 302446
2198 Utot 324614
2199 Utot 299980
2200 Utot 345438
2201 Utot 293009
2202 Utot 339444
2203 Utot 314127
2204 Utot 334541
2205 Utot 290329
2206 Utot 357876
2207 Utot 308127
2208 Utot 308618
2209 Utot 308437
2210 Utot 308821
2211 Utot 291415
2212 Utot 300669
2213 Utot 298220
2214 Utot 323808
2215 Utot 305780
2216 Utot 356949
2217 Utot 334875
2218 Utot 357952
2219 Utot 389575
2220 Utot 356991
2221 Utot 273025
2222 Utot 326558
2223 Utot 308484
2224 Utot 290030
2225 Utot 316019
2226 Utot 325821
2227 Utot 330867
2228 Utot 297444
2229 Utot 302025
2230 Utot 302070
2231 Utot 307003
2232 Utot 300301
2233 Utot 322126
2234 Utot 317568
2235 Utot 356008
2236 Utot 306036
2237 Utot 278731
2238 Utot 286212
2239 Utot 312864
2240 Utot 341969
2241 Utot 351786
2242 Utot 357307
2243 Utot 325934
2244 Utot 325360
2245 Utot 316615
2246 Utot 391850
2247 Utot 330101
2248 Utot 335710
2249 Utot 327606
2250 Utot 301609
2251 Utot 316549
2252 Utot 356192
2253 Utot 309868
2254 Utot 351468
2255 Utot 356278
2256 Utot 296714
2257 Utot 344894
2258 Utot 331528
2259 Utot 348262
2260 Utot 302099
2261 Utot 292562
2262 Utot 310666
2263 Utot 346489
2264 Utot 324871
2265 Utot 410117
2266 Utot 297194
2267 Utot 293533
2268 Utot 385341
2269 Utot 321711
2270 Utot 314296
2271 Utot 341009
2272 Utot 317528
2273 Utot 350810
2274 Utot 288151
2275 Utot 336337
2276 Utot 379722
2277 Utot 365840
2278 Utot 319704
2279 Utot 312930
2280 Utot 286197
2281 Utot 363368
2282 Utot 315759
2283 Utot 327088
2284 Utot 334799
2285 Utot 351255
2286 Utot 362647
2287 Utot 294392
2288 Utot 317360
2289 Utot 304386
2290 Utot 281141
2291 Utot 346274
2292 Utot 283323
2293 Utot 301548
2294 Utot 298057
2295 Utot 326887
2296 Utot 415603
2297 Utot 379446
2298 Utot 357888
2299 Utot 407257
2300 Utot 302909
2301 Utot 357315
2302 Utot 357535
2303 Utot 373895
2304 Utot 338641
2305 Utot 334763
2306 Utot 316342
2307 Utot 375828
2308 Utot 303494
2309 Utot 301754
2310 Utot 327314
2311 Utot 318441
2312 Utot 323989
2313 Utot 328035
2314 Utot 416664
2315 Utot 289839
2316 Utot 352407
2317 Utot 378312
2318 Utot 362126
2319 Utot 328916
2320 Utot 333667
2321 Utot 294200
2322 Utot 340876
2323 Utot 288566
2324 Utot 357067
2325 Utot 315994
2326 Utot 387645
2327 Utot 285343
2328 Utot 340146
2329 Utot 323938
2330 Utot 373832
2331 Utot 337899
2332 Utot 356148
2333 Utot 324131
2334 Utot 406344
2335 Utot 321856
2336 Utot 332332
2337 Utot 315291
2338 Utot 299107
2339 Utot 363350
2340 Utot 291736
2341 Utot 316364
2342 Utot 353517
2343 Utot 293461
2344 Utot 350956
2345 Utot 295160
2346 Utot 308204
2347 Utot 407597
2348 Utot 344111
2349 Utot 345901
2350 Utot 295549
2351 Utot 345685
2352 Utot 344540
2353 Utot 338519
2354 Utot 302417
2355 Utot 296779
2356 Utot 325321
2357 Utot 305732
2358 Utot 338419
2359 Utot 332408
2360 Utot 351895
2361 Utot 316381
2362 Utot 315534
2363 Utot 297712
2364 Utot 340178
2365 Utot 306256
2366 Utot 390943
2367 Utot 356565
2368 Utot 349197
2369 Utot 372024
2370 Utot 310917
2371 Utot 375285
2372 Utot 307348
2373 Utot 419285
2374 Utot 476484
2375 Utot 353559
2376 Utot 311484
2377 Utot 314129
2378 Utot 301752
2379 Utot 319487
2380 Utot 300092
2381 Utot 296767
2382 Utot 283133
2383 Utot 324075
2384 Utot 320986
2385 Utot 307020
2386 Utot 334464
2387 Utot 399582
2388 Utot 307513
2389 Utot 285235
2390 Utot 319938
2391 Utot 344531
2392 Utot 300440
2393 Utot 309951
2394 Utot 277340
2395 Utot 412289
2396 Utot 349777
2397 Utot 310070
2398 Utot 301207
2399 Utot 312370
2400 Utot 340357
2401 Utot 316631
2402 Utot 279655
2403 Utot 343530
2404 Utot 369301
2405 Utot 304123
2406 Utot 308121
2407 Utot 365170
2408 Utot 327560
2409 Utot 285745
2410 Utot 299132
2411 Utot 286687
2412 Utot 316385
2413 Utot 292914
2414 Utot 350548
2415 Utot 325824
2416 Utot 280876
2417 Utot 329218
2418 Utot 299642
2419 Utot 348507
2420 Utot 306622
2421 Utot 340908
2422 Utot 311627
2423 Utot 363953
2424 Utot 320334
2425 Utot 346383
2426 Utot 295049
2427 Utot 324247
2428 Utot 284064
2429 Utot 345860
2430 Utot 309535
2431 Utot 380036
2432 Utot 321673
2433 Utot 344295
2434 Utot 332290
2435 Utot 319206
2436 Utot 317597
2437 Utot 335359
2438 Utot 376673
2439 Utot 373913
2440 Utot 304395
2441 Utot 312520
2442 Utot 298670
2443 Utot 317810
2444 Utot 305980
2445 Utot 349573
2446 Utot 288972
2447 Utot 305697
2448 Utot 292343
2449 Utot 380358
2450 Utot 360865
2451 Utot 322000
2452 Utot 334979
2453 Utot 345486
2454 Utot 301574
2455 Utot 382049
2456 Utot 330974
2457 Utot 367384
2458 Utot 353788
2459 Utot 337319
2460 Utot 326541
2461 Utot 305704
2462 Utot 319697
2463 Utot 297213
2464 Utot 322954
2465 Utot 296552
2466 Utot 325281
2467 Utot 307731
2468 Utot 360441
2469 Utot 303613
2470 Utot 330149
2471 Utot 328412
2472 Utot 302975
2473 Utot 355204
2474 Utot 311249
2475 Utot 367005
2476 Utot 348155
2477 Utot 374402
2478 Utot 367162
2479 Utot 320055
2480 Utot 403928
2481 Utot 331961
2482 Utot 356390
2483 Utot 321698
2484 Utot 342538
2485 Utot 333227
2486 Utot 367606
2487 Utot 310228
2488 Utot 349392
2489 Utot 372238
2490 Utot 381296
2491 Utot 306524
2492 Utot 349279
2493 Utot 343262
2494 Utot 311257
2495 Utot 299487
2496 Utot 314603
2497 Utot 432623
2498 Utot 337705
2499 Utot 340622
2500 Utot 333874
2501 Utot 327032
2502 Utot 354372
2503 Utot 332923
2504 Utot 285615
2505 Utot 331230
2506 Utot 305788
2507 Utot 359772
2508 Utot 315392
2509 Utot 361988
2510 Utot 309968
2511 Utot 331694
2512 Utot 357136
2513 Utot 308074
2514 Utot 326217
2515 Utot 333206
2516 Utot 321333
2517 Utot 345956
2518 Utot 367400
2519 Utot 279977
2520 Utot 309408
2521 Utot 306355
2522 Utot 396534
2523 Utot 336680
2524 Utot 332058
2525 Utot 320811
2526 Utot 335286
2527 Utot 355693
2528 Utot 328720
2529 Utot 299908
2530 Utot 323302
2531 Utot 345531
2532 Utot 345926
2533 Utot 318605
2534 Utot 352268
2535 Utot 372224
2536 Utot 296970
2537 Utot 361236
2538 Utot 314224
2539 Utot 282920
2540 Utot 341616
2541 Utot 359282
2542 Utot 315992
2543 Utot 344122
2544 Utot 302330
2545 Utot 278331
2546 Utot 398390
2547 Utot 341507
2548 Utot 312910
2549 Utot 389677
2550 Utot 379973
2551 Utot 337651
2552 Utot 311340
2553 Utot 355012
2554 Utot 357384
2555 Utot 298752
2556 Utot 309742
2557 Utot 346350
2558 Utot 357619
2559 Utot 297815
2560 Utot 279312
2561 Utot 381545
2562 Utot 376666
2563 Utot 342853
2564 Utot 282129
2565 Utot 331463
2566 Utot 346005
2567 Utot 273292
2568 Utot 324249
2569 Utot 269480
2570 Utot 448914
2571 Utot 349079
2572 Utot 328385
2573 Utot 348065
2574 Utot 380656
2575 Utot 363969
2576 Utot 330960
2577 Utot 352372
2578 Utot 321667
2579 Utot 336897
2580 Utot 398624
2581 Utot 303547
2582 Utot 310982
2583 Utot 386417
2584 Utot 313385
2585 Utot 326863
2586 Utot 352560
2587 Utot 311883
2588 Utot 363299
2589 Utot 369588
2590 Utot 343330
2591 Utot 348475
2592 Utot 317071
2593 Utot 334045
2594 Utot 351029
2595 Utot 306036
2596 Utot 305454
2597 Utot 328396
2598 Utot 316699
2599 Utot 288310
2600 Utot 290060
2601 Utot 338248
2602 Utot 304123
2603 Utot 356624
2604 Utot 322798
2605 Utot 310217
2606 Utot 428281
2607 Utot 329939
2608 Utot 329464
2609 Utot 297981
2610 Utot 299900
2611 Utot 333086
2612 Utot 339697
2613 Utot 338916
2614 Utot 296243
2615 Utot 292888
2616 Utot 319689
2617 Utot 290094
2618 Utot 315339
2619 Utot 365318
2620 Utot 340058
2621 Utot 337985
2622 Utot 364288
2623 Utot 310991
2624 Utot 327937
2625 Utot 322752
2626 Utot 345994
2627 Utot 337038
2628 Utot 329748
2629 Utot 300185
2630 Utot 321292
2631 Utot 371548
2632 Utot 291385
2633 Utot 359773
2634 Utot 332523
2635 Utot 307698
2636 Utot 310165
2637 Utot 350665
2638 Utot 457974
2639 Utot 347319
2640 Utot 327932
2641 Utot 322040
2642 Utot 328220
2643 Utot 336949
2644 Utot 369890
2645 Utot 324745
2646 Utot 347867
2647 Utot 354970
2648 Utot 276917
2649 Utot 295583
2650 Utot 404440
2651 Utot 337846
2652 Utot 364096
2653 Utot 356005
2654 Utot 370422
2655 Utot 334981
2656 Utot 291833
2657 Utot 359173
2658 Utot 287544
2659 Utot 303292
2660 Utot 418610
2661 Utot 305488
2662 Utot 335691
2663 Utot 333985
2664 Utot 306209
2665 Utot 307896
2666 Utot 279545
2667 Utot 351534
2668 Utot 299949
2669 Utot 385540
2670 Utot 310544
2671 Utot 406688
2672 Utot 332085
2673 Utot 344065
2674 Utot 313357
2675 Utot 286596
2676 Utot 434481
2677 Utot 367144
2678 Utot 316988
2679 Utot 321821
2680 Utot 448670
2681 Utot 312296
2682 Utot 383590
2683 Utot 288959
2684 Utot 327462
2685 Utot 349514
2686 Utot 328395
2687 Utot 307326
2688 Utot 396224
2689 Utot 351189
2690 Utot 365509
2691 Utot 323157
2692 Utot 370921
2693 Utot 347205
2694 Utot 334517
2695 Utot 384866
2696 Utot 390435
2697 Utot 395724
2698 Utot 308677
2699 Utot 359752
2700 Utot 302764
2701 Utot 305809
2702 Utot 331011
2703 Utot 321387
2704 Utot 301656
2705 Utot 295932
2706 Utot 331475
2707 Utot 314487
2708 Utot 296313
2709 Utot 335578
2710 Utot 289850
2711 Utot 368361
2712 Utot 298102
2713 Utot 306965
2714 Utot 365488
2715 Utot 359019
2716 Utot 317118
2717 Utot 311528
2718 Utot 351755
2719 Utot 334244
2720 Utot 301279
2721 Utot 321373
2722 Utot 331872
2723 Utot 312352
2724 Utot 307577
2725 Utot 397483
2726 Utot 324201
2727 Utot 316372
2728 Utot 389269
2729 Utot 392427
2730 Utot 318036
2731 Utot 335621
2732 Utot 362748
2733 Utot 322971
2734 Utot 377025
2735 Utot 314083
2736 Utot 427448
2737 Utot 401825
2738 Utot 302785
2739 Utot 384300
2740 Utot 304686
2741 Utot 389220
2742 Utot 383912
2743 Utot 330826
2744 Utot 308045
2745 Utot 362316
2746 Utot 296879
2747 Utot 292195
2748 Utot 423086
2749 Utot 318007
2750 Utot 378460
2751 Utot 336076
2752 Utot 348937
2753 Utot 324299
2754 Utot 312318
2755 Utot 301486
2756 Utot 331183
2757 Utot 324503
2758 Utot 329487
2759 Utot 329308
2760 Utot 324337
2761 Utot 300380
2762 Utot 284035
2763 Utot 307435
2764 Utot 300701
2765 Utot 320293
2766 Utot 324295
2767 Utot 300352
2768 Utot 312637
2769 Utot 386683
2770 Utot 353106
2771 Utot 315387
2772 Utot 401215
2773 Utot 274006
2774 Utot 413334
2775 Utot 447433
2776 Utot 329634
2777 Utot 398977
2778 Utot 305928
2779 Utot 306383
2780 Utot 342082
2781 Utot 293677
2782 Utot 358952
2783 Utot 317530
2784 Utot 342158
2785 Utot 267857
2786 Utot 455906
2787 Utot 306204
2788 Utot 369667
2789 Utot 403073
2790 Utot 380809
2791 Utot 335864
2792 Utot 306906
2793 Utot 290812
2794 Utot 278492
2795 Utot 428684
2796 Utot 324499
2797 Utot 394990
2798 Utot 363705
2799 Utot 327803
2800 Utot 323476
2801 Utot 407097
2802 Utot 307036
2803 Utot 318617
2804 Utot 316777
2805 Utot 323049
2806 Utot 327750
2807 Utot 304361
2808 Utot 340899
2809 Utot 355781
2810 Utot 322863
2811 Utot 396784
2812 Utot 328448
2813 Utot 290679
2814 Utot 402097
2815 Utot 347898
2816 Utot 307049
2817 Utot 297754
2818 Utot 419577
2819 Utot 392806
2820 Utot 333757
2821 Utot 311490
2822 Utot 330883
2823 Utot 304042
2824 Utot 312401
2825 Utot 325522
2826 Utot 401083
2827 Utot 326901
2828 Utot 294541
2829 Utot 299721
2830 Utot 341064
2831 Utot 356882
2832 Utot 334645
2833 Utot 321742
2834 Utot 324504
2835 Utot 338424
2836 Utot 335130
2837 Utot 298131
2838 Utot 306643
2839 Utot 369257
2840 Utot 313351
2841 Utot 317987
2842 Utot 365492
2843 Utot 357205
2844 Utot 307828
2845 Utot 344029
2846 Utot 323810
2847 Utot 379680
2848 Utot 313963
2849 Utot 310491
2850 Utot 356900
2851 Utot 346051
2852 Utot 362870
2853 Utot 303025
2854 Utot 398417
2855 Utot 338707
2856 Utot 386326
2857 Utot 326103
2858 Utot 298597
2859 Utot 292277
2860 Utot 389348
2861 Utot 340688
2862 Utot 304109
2863 Utot 389420
2864 Utot 303204
2865 Utot 376158
2866 Utot 308016
2867 Utot 300853
2868 Utot 381365
2869 Utot 331021
2870 Utot 307916
2871 Utot 328270
2872 Utot 304152
2873 Utot 349338
2874 Utot 343978
2875 Utot 301582
2876 Utot 386999
2877 Utot 316343
2878 Utot 287613
2879 Utot 324413
2880 Utot 342084
2881 Utot 381902
2882 Utot 354023
2883 Utot 332280
2884 Utot 335288
2885 Utot 360645
2886 Utot 374387
2887 Utot 317267
2888 Utot 312716
2889 Utot 298443
2890 Utot 306182
2891 Utot 318463
2892 Utot 379340
2893 Utot 291429
2894 Utot 340257
2895 Utot 344356
2896 Utot 317358
2897 Utot 351550
2898 Utot 363069
2899 Utot 328874
2900 Utot 290728
2901 Utot 303373
2902 Utot 324660
2903 Utot 352722
2904 Utot 347438
2905 Utot 289186
2906 Utot 421970
2907 Utot 311688
2908 Utot 327785
2909 Utot 334496
2910 Utot 320181
2911 Utot 381906
2912 Utot 331946
2913 Utot 312195
2914 Utot 340532
2915 Utot 319226
2916 Utot 311407
2917 Utot 265295
2918 Utot 335904
2919 Utot 382823
2920 Utot 308403
2921 Utot 355459
2922 Utot 339732
2923 Utot 359448
2924 Utot 338219
2925 Utot 298297
2926 Utot 331514
2927 Utot 359874
2928 Utot 374970
2929 Utot 306474
2930 Utot 356319
2931 Utot 299423
2932 Utot 319957
2933 Utot 391460
2934 Utot 332989
2935 Utot 306198
2936 Utot 293734
2937 Utot 345319
2938 Utot 307409
2939 Utot 303682
2940 Utot 353077
2941 Utot 351876
2942 Utot 332884
2943 Utot 341481
2944 Utot 312220
2945 Utot 369389
2946 Utot 316744
2947 Utot 327651
2948 Utot 341810
2949 Utot 319687
2950 Utot 364331
2951 Utot 310131
2952 Utot 287008
2953 Utot 295205
2954 Utot 342210
2955 Utot 351253
2956 Utot 355139
2957 Utot 323624
2958 Utot 303423
2959 Utot 297732
2960 Utot 315539
2961 Utot 392622
2962 Utot 338320
2963 Utot 348380
2964 Utot 320716
2965 Utot 350101
2966 Utot 296926
2967 Utot 370637
2968 Utot 318967
2969 Utot 321977
2970 Utot 353660
2971 Utot 282066
2972 Utot 355708
2973 Utot 301878
2974 Utot 308910
2975 Utot 364580
2976 Utot 290600
2977 Utot 290474
2978 Utot 312680
2979 Utot 353469
2980 Utot 353544
2981 Utot 346706
2982 Utot 303516
2983 Utot 304704
2984 Utot 376727
2985 Utot 334358
2986 Utot 323934
2987 Utot 301255
2988 Utot 371712
2989 Utot 303543
2990 Utot 281768
2991 Utot 365937
2992 Utot 313431
2993 Utot 295733
2994 Utot 341112
2995 Utot 298140
2996 Utot 305757
2997 Utot 325730
2998 Utot 307533
2999 Utot 302739
3000 Utot 363655
3001 Utot 356432
3002 Utot 279722
3003 Utot 378123
3004 Utot 345277
3005 Utot 282637
3006 Utot 326250
3007 Utot 351954
3008 Utot 297872
3009 Utot 358649
3010 Utot 380600
3011 Utot 309284
3012 Utot 347822
3013 Utot 328559
3014 Utot 296614
3015 Utot 298282
3016 Utot 349588
3017 Utot 373187
3018 Utot 291692
3019 Utot 350117
3020 Utot 276915
3021 Utot 338728
3022 Utot 375863
3023 Utot 316293
3024 Utot 308053
3025 Utot 325209
3026 Utot 376278
3027 Utot 276703
3028 Utot 341085
3029 Utot 348277
3030 Utot 352384
3031 Utot 369182
3032 Utot 327018
3033 Utot 327237
3034 Utot 384925
3035 Utot 381472
3036 Utot 318235
3037 Utot 337309
3038 Utot 333631
3039 Utot 340928
3040 Utot 301630
3041 Utot 311142
3042 Utot 376344
3043 Utot 332280
3044 Utot 400402
3045 Utot 331271
3046 Utot 351284
3047 Utot 358612
3048 Utot 324147
3049 Utot 309347
3050 Utot 542497
3051 Utot 325966
3052 Utot 303762
3053 Utot 339459
3054 Utot 274581
3055 Utot 404608
3056 Utot 352534
3057 Utot 292173
3058 Utot 302587
3059 Utot 330452
3060 Utot 288009
3061 Utot 352581
3062 Utot 348950
3063 Utot 286128
3064 Utot 339634
3065 Utot 316846
3066 Utot 326374
3067 Utot 339921
3068 Utot 335427
3069 Utot 366086
3070 Utot 302158
3071 Utot 307845
3072 Utot 322559
3073 Utot 318920
3074 Utot 324497
3075 Utot 313554
3076 Utot 422264
3077 Utot 361324
3078 Utot 320271
3079 Utot 304514
3080 Utot 330746
3081 Utot 361779
3082 Utot 312802
3083 Utot 313269
3084 Utot 329671
3085 Utot 343294
3086 Utot 292483
3087 Utot 309879
3088 Utot 341085
3089 Utot 309959
3090 Utot 343669
3091 Utot 323173
3092 Utot 334006
3093 Utot 338286
3094 Utot 341085
3095 Utot 383030
3096 Utot 339404
3097 Utot 362743
3098 Utot 348192
3099 Utot 362200
3100 Utot 395817
3101 Utot 326958
3102 Utot 333821
3103 Utot 337425
3104 Utot 336894
3105 Utot 332025
3106 Utot 312956
3107 Utot 376160
3108 Utot 348092
3109 Utot 298064
3110 Utot 337183
3111 Utot 326821
3112 Utot 322437
3113 Utot 324089
3114 Utot 312399
3115 Utot 346332
3116 Utot 301295
3117 Utot 407612
3118 Utot 315526
3119 Utot 350808
3120 Utot 305171
3121 Utot 270708
3122 Utot 321061
3123 Utot 343626
3124 Utot 349408
3125 Utot 358147
3126 Utot 379307
3127 Utot 307876
3128 Utot 315994
3129 Utot 341473
3130 Utot 332195
3131 Utot 329543
3132 Utot 297184
3133 Utot 350565
3134 Utot 316479
3135 Utot 290499
3136 Utot 346128
3137 Utot 362436
3138 Utot 306733
3139 Utot 354593
3140 Utot 333476
3141 Utot 403568
3142 Utot 286604
3143 Utot 303657
3144 Utot 352529
3145 Utot 384743
3146 Utot 337013
3147 Utot 339598
3148 Utot 347228
3149 Utot 406492
3150 Utot 356186
3151 Utot 283026
3152 Utot 304464
3153 Utot 312458
3154 Utot 373510
3155 Utot 325645
3156 Utot 288227
3157 Utot 313369
3158 Utot 368165
3159 Utot 279763
3160 Utot 335461
3161 Utot 432928
3162 Utot 332816
3163 Utot 365120
3164 Utot 382422
3165 Utot 324081
3166 Utot 305014
3167 Utot 302938
3168 Utot 378115
3169 Utot 329343
3170 Utot 321697
3171 Utot 366475
3172 Utot 273692
3173 Utot 348011
3174 Utot 279425
3175 Utot 315705
3176 Utot 369029
3177 Utot 336548
3178 Utot 319595
3179 Utot 309194
3180 Utot 326912
3181 Utot 374071
3182 Utot 309876
3183 Utot 309754
3184 Utot 358281
3185 Utot 310408
3186 Utot 350441
3187 Utot 294413
3188 Utot 291355
3189 Utot 379759
3190 Utot 338920
3191 Utot 311359
3192 Utot 299537
3193 Utot 324955
3194 Utot 281939
3195 Utot 293053
3196 Utot 325793
3197 Utot 296337
3198 Utot 269922
3199 Utot 324708
3200 Utot 321148
3201 Utot 359586
3202 Utot 335728
3203 Utot 313335
3204 Utot 339869
3205 Utot 320590
3206 Utot 288340
3207 Utot 354909
3208 Utot 366197
3209 Utot 299305
3210 Utot 334382
3211 Utot 343591
3212 Utot 403668
3213 Utot 285140
3214 Utot 410742
3215 Utot 327168
3216 Utot 350133
3217 Utot 326029
3218 Utot 321610
3219 Utot 327377
3220 Utot 341994
3221 Utot 316807
3222 Utot 343806
3223 Utot 339381
3224 Utot 347769
3225 Utot 451867
3226 Utot 315625
3227 Utot 308671
3228 Utot 310230
3229 Utot 348584
3230 Utot 325596
3231 Utot 282392
3232 Utot 334564
3233 Utot 331866
3234 Utot 311160
3235 Utot 339797
3236 Utot 306148
3237 Utot 303665
3238 Utot 309704
3239 Utot 296318
3240 Utot 320766
3241 Utot 337564
3242 Utot 507633
3243 Utot 320131
3244 Utot 293595
3245 Utot 307914
3246 Utot 360582
3247 Utot 483391
3248 Utot 286223
3249 Utot 345869
3250 Utot 334321
3251 Utot 289595
3252 Utot 321240
3253 Utot 330318
3254 Utot 411721
3255 Utot 368012
3256 Utot 353730
3257 Utot 319001
3258 Utot 287864
3259 Utot 303617
3260 Utot 309689
3261 Utot 345073
3262 Utot 299595
3263 Utot 347194
3264 Utot 290507
3265 Utot 320553
3266 Utot 323956
3267 Utot 365779
3268 Utot 318236
3269 Utot 338801
3270 Utot 351352
3271 Utot 297506
3272 Utot 340824
3273 Utot 301519
3274 Utot 296073
3275 Utot 322307
3276 Utot 305416
3277 Utot 289577
3278 Utot 319865
3279 Utot 291017
3280 Utot 350348
3281 Utot 291117
3282 Utot 319175
3283 Utot 349705
3284 Utot 331130
3285 Utot 354829
3286 Utot 344167
3287 Utot 393198
3288 Utot 316021
3289 Utot 305136
3290 Utot 320995
3291 Utot 306873
3292 Utot 314984
3293 Utot 316933
3294 Utot 325476
3295 Utot 329887
3296 Utot 326550
3297 Utot 322599
3298 Utot 300208
3299 Utot 308289
3300 Utot 282234
3301 Utot 343570
3302 Utot 305630
3303 Utot 317130
3304 Utot 325461
3305 Utot 377730
3306 Utot 331395
3307 Utot 336283
3308 Utot 414984
3309 Utot 309861
3310 Utot 297540
3311 Utot 348386
3312 Utot 318674
3313 Utot 332241
3314 Utot 316892
3315 Utot 282132
3316 Utot 366395
3317 Utot 323449
3318 Utot 311130
3319 Utot 367936
3320 Utot 354595
3321 Utot 334223
3322 Utot 300898
3323 Utot 310964
3324 Utot 346291
3325 Utot 274532
3326 Utot 340132
3327 Utot 305848
3328 Utot 356113
3329 Utot 337983
3330 Utot 320035
3331 Utot 343395
3332 Utot 302998
3333 Utot 358437
3334 Utot 328136
3335 Utot 336285
3336 Utot 329448
3337 Utot 301197
3338 Utot 351606
3339 Utot 347226
3340 Utot 397856
3341 Utot 311941
3342 Utot 392597
3343 Utot 312895
3344 Utot 344611
3345 Utot 336046
3346 Utot 277697
3347 Utot 386395
3348 Utot 351065
3349 Utot 301421
3350 Utot 364125
3351 Utot 372102
3352 Utot 295735
3353 Utot 270507
3354 Utot 359570
3355 Utot 331656
3356 Utot 327643
3357 Utot 356744
3358 Utot 308299
3359 Utot 341044
3360 Utot 345805
3361 Utot 315329
3362 Utot 292270
3363 Utot 313618
3364 Utot 348615
3365 Utot 301818
3366 Utot 316265
3367 Utot 312113
3368 Utot 328124
3369 Utot 319163
3370 Utot 303996
3371 Utot 318729
3372 Utot 332602
3373 Utot 340544
3374 Utot 328439
3375 Utot 318486
3376 Utot 336763
3377 Utot 323781
3378 Utot 299927
3379 Utot 385072
3380 Utot 381405
3381 Utot 340967
3382 Utot 404824
3383 Utot 300418
3384 Utot 321577
3385 Utot 346170
3386 Utot 342747
3387 Utot 318681
3388 Utot 368686
3389 Utot 321765
3390 Utot 304749
3391 Utot 318181
3392 Utot 323024
3393 Utot 290334
3394 Utot 367255
3395 Utot 322077
3396 Utot 333151
3397 Utot 273663
3398 Utot 421488
3399 Utot 281060
3400 Utot 328853
3401 Utot 340083
3402 Utot 323511
3403 Utot 365817
3404 Utot 398614
3405 Utot 313396
3406 Utot 361099
3407 Utot 318130
3408 Utot 308627
3409 Utot 335475
3410 Utot 304611
3411 Utot 336832
3412 Utot 325946
3413 Utot 305419
3414 Utot 339600
3415 Utot 284182
3416 Utot 300845
3417 Utot 317903
3418 Utot 373225
3419 Utot 320429
3420 Utot 335270
3421 Utot 316498
3422 Utot 331187
3423 Utot 342105
3424 Utot 329928
3425 Utot 307180
3426 Utot 291055
3427 Utot 325653
3428 Utot 287982
3429 Utot 329282
3430 Utot 327688
3431 Utot 304087
3432 Utot 394472
3433 Utot 298653
3434 Utot 297499
3435 Utot 381106
3436 Utot 386387
3437 Utot 303618
3438 Utot 361920
3439 Utot 362756
3440 Utot 295479
3441 Utot 337286
3442 Utot 313101
3443 Utot 328132
3444 Utot 314601
3445 Utot 320516
3446 Utot 307849
3447 Utot 317970
3448 Utot 341075
3449 Utot 308716
3450 Utot 327974
3451 Utot 344321
3452 Utot 331941
3453 Utot 375869
3454 Utot 284519
3455 Utot 350947
3456 Utot 325400
3457 Utot 362795
3458 Utot 441758
3459 Utot 319149
3460 Utot 292337
3461 Utot 309723
3462 Utot 307216
3463 Utot 316209
3464 Utot 396946
3465 Utot 397341
3466 Utot 344329
3467 Utot 295809
3468 Utot 330915
3469 Utot 282602
3470 Utot 316676
3471 Utot 394063
3472 Utot 348225
3473 Utot 332458
3474 Utot 357927
3475 Utot 316909
3476 Utot 330347
3477 Utot 357280
3478 Utot 283629
3479 Utot 340119
3480 Utot 360729
3481 Utot 363478
3482 Utot 317632
3483 Utot 339109
3484 Utot 303488
3485 Utot 357606
3486 Utot 286332
3487 Utot 344545
3488 Utot 299782
3489 Utot 354757
3490 Utot 301094
3491 Utot 300398
3492 Utot 348916
3493 Utot 314319
3494 Utot 316382
3495 Utot 348474
3496 Utot 281663
3497 Utot 317618
3498 Utot 307333
3499 Utot 291148
3500 Utot 360243
3501 Utot 343744
3502 Utot 351771
3503 Utot 376844
3504 Utot 348113
3505 Utot 294999
3506 Utot 306084
3507 Utot 349652
3508 Utot 304864
3509 Utot 380790
3510 Utot 306550
3511 Utot 397519
3512 Utot 389084
3513 Utot 358750
3514 Utot 340377
3515 Utot 379207
3516 Utot 276941
3517 Utot 307811
3518 Utot 299774
3519 Utot 328458
3520 Utot 357701
3521 Utot 306406
3522 Utot 321261
3523 Utot 376552
3524 Utot 381034
3525 Utot 363904
3526 Utot 362287
3527 Utot 312884
3528 Utot 322978
3529 Utot 331578
3530 Utot 308347
3531 Utot 316224
3532 Utot 364893
3533 Utot 319497
3534 Utot 380975
3535 Utot 335344
3536 Utot 384121
3537 Utot 305382
3538 Utot 314667
3539 Utot 367686
3540 Utot 384884
3541 Utot 354425
3542 Utot 331229
3543 Utot 291962
3544 Utot 279292
3545 Utot 439673
3546 Utot 369066
3547 Utot 360256
3548 Utot 290205
3549 Utot 297244
3550 Utot 349317
3551 Utot 333662
3552 Utot 310414
3553 Utot 322014
3554 Utot 367284
3555 Utot 311984
3556 Utot 316064
3557 Utot 366493
3558 Utot 322368
3559 Utot 285575
3560 Utot 366119
3561 Utot 363280
3562 Utot 402083
3563 Utot 312222
3564 Utot 354162
3565 Utot 397972
3566 Utot 354867
3567 Utot 388625
3568 Utot 343378
3569 Utot 319130
3570 Utot 336047
3571 Utot 354712
3572 Utot 306112
3573 Utot 338774
3574 Utot 305706
3575 Utot 370417
3576 Utot 293058
3577 Utot 328866
3578 Utot 327854
3579 Utot 317285
3580 Utot 326481
3581 Utot 327477
3582 Utot 358720
3583 Utot 323159
3584 Utot 383356
3585 Utot 318950
3586 Utot 322772
3587 Utot 309559
3588 Utot 314231
3589 Utot 287773
3590 Utot 324311
3591 Utot 391160
3592 Utot 307764
3593 Utot 270344
3594 Utot 376168
3595 Utot 313359
3596 Utot 299941
3597 Utot 298950
3598 Utot 426849
3599 Utot 344402
3600 Utot 310006
3601 Utot 401936
3602 Utot 416056
3603 Utot 301053
3604 Utot 309882
3605 Utot 387324
3606 Utot 310696
3607 Utot 349077
3608 Utot 333642
3609 Utot 387137
3610 Utot 345941
3611 Utot 298167
3612 Utot 317640
3613 Utot 301889
3614 Utot 276735
3615 Utot 354978
3616 Utot 302425
3617 Utot 299753
3618 Utot 345337
3619 Utot 317218
3620 Utot 368374
3621 Utot 305388
3622 Utot 336943
3623 Utot 307347
3624 Utot 331343
3625 Utot 314723
3626 Utot 405595
3627 Utot 292076
3628 Utot 314503
3629 Utot 289285
3630 Utot 345087
3631 Utot 289932
3632 Utot 348282
3633 Utot 349601
3634 Utot 403309
3635 Utot 354012
3636 Utot 318940
3637 Utot 400250
3638 Utot 312030
3639 Utot 311182
3640 Utot 352394
3641 Utot 323492
3642 Utot 287161
3643 Utot 317302
3644 Utot 356013
3645 Utot 308106
3646 Utot 308324
3647 Utot 328946
3648 Utot 327596
3649 Utot 397182
3650 Utot 359423
3651 Utot 327685
3652 Utot 351713
3653 Utot 315934
3654 Utot 302174
3655 Utot 280141
3656 Utot 324642
3657 Utot 316969
3658 Utot 335132
3659 Utot 319213
3660 Utot 309729
3661 Utot 338104
3662 Utot 315484
3663 Utot 369319
3664 Utot 290901
3665 Utot 306892
3666 Utot 350495
3667 Utot 307276
3668 Utot 344992
3669 Utot 314381
3670 Utot 319737
3671 Utot 312299
3672 Utot 351639
3673 Utot 397329
3674 Utot 344548
3675 Utot 343493
3676 Utot 295903
3677 Utot 363160
3678 Utot 341854
3679 Utot 318352
3680 Utot 387203
3681 Utot 338075
3682 Utot 282182
3683 Utot 360347
3684 Utot 311237
3685 Utot 303558
3686 Utot 318263
3687 Utot 342184
3688 Utot 276350
3689 Utot 341011
3690 Utot 288820
3691 Utot 387536
3692 Utot 375639
3693 Utot 364725
3694 Utot 330004
3695 Utot 324741
3696 Utot 312516
3697 Utot 343721
3698 Utot 342832
3699 Utot 283036
3700 Utot 356831
3701 Utot 304061
3702 Utot 337470
3703 Utot 311004
3704 Utot 334143
3705 Utot 325000
3706 Utot 329199
3707 Utot 388949
3708 Utot 282427
3709 Utot 284698
3710 Utot 415569
3711 Utot 322870
3712 Utot 342044
3713 Utot 297457
3714 Utot 299826
3715 Utot 302135
3716 Utot 370174
3717 Utot 323415
3718 Utot 308824
3719 Utot 299304
3720 Utot 360114
3721 Utot 337414
3722 Utot 412503
3723 Utot 289843
3724 Utot 346093
3725 Utot 325007
3726 Utot 319073
3727 Utot 346466
3728 Utot 289645
3729 Utot 330818
3730 Utot 348919
3731 Utot 345312
3732 Utot 361445
3733 Utot 293511
3734 Utot 292391
3735 Utot 355630
3736 Utot 304538
3737 Utot 321460
3738 Utot 389265
3739 Utot 296345
3740 Utot 329217
3741 Utot 318229
3742 Utot 436738
3743 Utot 334571
3744 Utot 330290
3745 Utot 307626
3746 Utot 366360
3747 Utot 319242
3748 Utot 380798
3749 Utot 317050
3750 Utot 372152
3751 Utot 291345
3752 Utot 305340
3753 Utot 342935
3754 Utot 278548
3755 Utot 279276
3756 Utot 405884
3757 Utot 319022
3758 Utot 302212
3759 Utot 378199
3760 Utot 330044
3761 Utot 304143
3762 Utot 320603
3763 Utot 292407
3764 Utot 327446
3765 Utot 339419
3766 Utot 329780
3767 Utot 308169
3768 Utot 431090
3769 Utot 315722
3770 Utot 323660
3771 Utot 296504
3772 Utot 386872
3773 Utot 360666
3774 Utot 355503
3775 Utot 290338
3776 Utot 366955
3777 Utot 294290
3778 Utot 342069
3779 Utot 301790
3780 Utot 409855
3781 Utot 336033
3782 Utot 352517
3783 Utot 362291
3784 Utot 320842
3785 Utot 288604
3786 Utot 297543
3787 Utot 351646
3788 Utot 371899
3789 Utot 305904
3790 Utot 353526
3791 Utot 353725
3792 Utot 320647
3793 Utot 341123
3794 Utot 359162
3795 Utot 335685
3796 Utot 342810
3797 Utot 302210
3798 Utot 372043
3799 Utot 271885
3800 Utot 322565
3801 Utot 363883
3802 Utot 345605
3803 Utot 295823
3804 Utot 293075
3805 Utot 319234
3806 Utot 317716
3807 Utot 311683
3808 Utot 316746
3809 Utot 357654
3810 Utot 293464
3811 Utot 346653
3812 Utot 269999
3813 Utot 337145
3814 Utot 329083
3815 Utot 404227
3816 Utot 300085
3817 Utot 336648
3818 Utot 314665
3819 Utot 315760
3820 Utot 329825
3821 Utot 346975
3822 Utot 340504
3823 Utot 308496
3824 Utot 367959
3825 Utot 343723
3826 Utot 375021
3827 Utot 366360
3828 Utot 328767
3829 Utot 394910
3830 Utot 335291
3831 Utot 289292
3832 Utot 323233
3833 Utot 347084
3834 Utot 307573
3835 Utot 332670
3836 Utot 363532
3837 Utot 330720
3838 Utot 324787
3839 Utot 286971
3840 Utot 356252
3841 Utot 337506
3842 Utot 365952
3843 Utot 404385
3844 Utot 326574
3845 Utot 453872
3846 Utot 313975
3847 Utot 307856
3848 Utot 348445
3849 Utot 330443
3850 Utot 323771
3851 Utot 292452
3852 Utot 352932
3853 Utot 328855
3854 Utot 297890
3855 Utot 372177
3856 Utot 304509
3857 Utot 299530
3858 Utot 305857
3859 Utot 326108
3860 Utot 293858
3861 Utot 464008
3862 Utot 395095
3863 Utot 336031
3864 Utot 426352
3865 Utot 345367
3866 Utot 353040
3867 Utot 302244
3868 Utot 360738
3869 Utot 371086
3870 Utot 285674
3871 Utot 336551
3872 Utot 337915
3873 Utot 310025
3874 Utot 324596
3875 Utot 292009
3876 Utot 356371
3877 Utot 353906
3878 Utot 364683
3879 Utot 340141
3880 Utot 391484
3881 Utot 350498
3882 Utot 397833
3883 Utot 327955
3884 Utot 339472
3885 Utot 367942
3886 Utot 333585
3887 Utot 315881
3888 Utot 300706
3889 Utot 317387
3890 Utot 342830
3891 Utot 313756
3892 Utot 376214
3893 Utot 320242
3894 Utot 305577
3895 Utot 324042
3896 Utot 298757
3897 Utot 287757
3898 Utot 344067
3899 Utot 371772
3900 Utot 354151
3901 Utot 320112
3902 Utot 331728
3903 Utot 363959
3904 Utot 346054
3905 Utot 315971
3906 Utot 377354
3907 Utot 278391
3908 Utot 331453
3909 Utot 348334
3910 Utot 340336
3911 Utot 273509
3912 Utot 301418
3913 Utot 321620
3914 Utot 340456
3915 Utot 355926
3916 Utot 370301
3917 Utot 296202
3918 Utot 328190
3919 Utot 350949
3920 Utot 306297
3921 Utot 293520
3922 Utot 322917
3923 Utot 303168
3924 Utot 388624
3925 Utot 350028
3926 Utot 302126
3927 Utot 338866
3928 Utot 301575
3929 Utot 350116
3930 Utot 314688
3931 Utot 366622
3932 Utot 287485
3933 Utot 275805
3934 Utot 280636
3935 Utot 279532
3936 Utot 303832
3937 Utot 408114
3938 Utot 319999
3939 Utot 306067
3940 Utot 286646
3941 Utot 343150
3942 Utot 327889
3943 Utot 316710
3944 Utot 309393
3945 Utot 300881
3946 Utot 321724
3947 Utot 392933
3948 Utot 318407
3949 Utot 388614
3950 Utot 292722
3951 Utot 370785
3952 Utot 364124
3953 Utot 304116
3954 Utot 341516
3955 Utot 319390
3956 Utot 427070
3957 Utot 303459
3958 Utot 317078
3959 Utot 293655
3960 Utot 306368
3961 Utot 327389
3962 Utot 420568
3963 Utot 368079
3964 Utot 301262
3965 Utot 368563
3966 Utot 396256
3967 Utot 348312
3968 Utot 294767
3969 Utot 315575
3970 Utot 333494
3971 Utot 295763
3972 Utot 321683
3973 Utot 283401
3974 Utot 332883
3975 Utot 338721
3976 Utot 287182
3977 Utot 388965
3978 Utot 295082
3979 Utot 286024
3980 Utot 343088
3981 Utot 278615
3982 Utot 320835
3983 Utot 369944
3984 Utot 360239
3985 Utot 295208
3986 Utot 344625
3987 Utot 359397
3988 Utot 338675
3989 Utot 287861
3990 Utot 330360
3991 Utot 343033
3992 Utot 335524
3993 Utot 303065
3994 Utot 319458
3995 Utot 303037
3996 Utot 364017
3997 Utot 282952
3998 Utot 289987
3999 Utot 356095
4000 Utot 320999
4001 Utot 309517
4002 Utot 312588
4003 Utot 322867
4004 Utot 327796
4005 Utot 326815
4006 Utot 322541
4007 Utot 306319
4008 Utot 354241
4009 Utot 362107
4010 Utot 324709
4011 Utot 318138
4012 Utot 320788
4013 Utot 308461
4014 Utot 288560
4015 Utot 292402
4016 Utot 309415
4017 Utot 368988
4018 Utot 350851
4019 Utot 340069
4020 Utot 269893
4021 Utot 334923
4022 Utot 325517
4023 Utot 309505
4024 Utot 301407
4025 Utot 362042
4026 Utot 321308
4027 Utot 366375
4028 Utot 309831
4029 Utot 295085
4030 Utot 348947
4031 Utot 326073
4032 Utot 313725
4033 Utot 296369
4034 Utot 368794
4035 Utot 402292
4036 Utot 311035
4037 Utot 380131
4038 Utot 332482
4039 Utot 287965
4040 Utot 349126
4041 Utot 363205
4042 Utot 294552
4043 Utot 342943
4044 Utot 382680
4045 Utot 350504
4046 Utot 322236
4047 Utot 312312
4048 Utot 370549
4049 Utot 330637
4050 Utot 332342
4051 Utot 333639
4052 Utot 351810
4053 Utot 336903
4054 Utot 339000
4055 Utot 308495
4056 Utot 320248
4057 Utot 396263
4058 Utot 302372
4059 Utot 286963
4060 Utot 328195
4061 Utot 350295
4062 Utot 294354
4063 Utot 435149
4064 Utot 345277
4065 Utot 315508
4066 Utot 274793
4067 Utot 286483
4068 Utot 329077
4069 Utot 356805
4070 Utot 397268
4071 Utot 355933
4072 Utot 323752
4073 Utot 326613
4074 Utot 430761
4075 Utot 303874
4076 Utot 336579
4077 Utot 288161
4078 Utot 381308
4079 Utot 386321
4080 Utot 331884
4081 Utot 314846
4082 Utot 299728
4083 Utot 337055
4084 Utot 340944
4085 Utot 361206
4086 Utot 342136
4087 Utot 338354
4088 Utot 300555
4089 Utot 330982
4090 Utot 305461
4091 Utot 284286
4092 Utot 351729
4093 Utot 410143
4094 Utot 343282
4095 Utot 339348
4096 Utot 291482
4097 Utot 311604
4098 Utot 328764
4099 Utot 326003
4100 Utot 322338
4101 Utot 300163
4102 Utot 314485
4103 Utot 358970
4104 Utot 331451
4105 Utot 397346
4106 Utot 322603
4107 Utot 295226
4108 Utot 274526
4109 Utot 278609
4110 Utot 321958
4111 Utot 411542
4112 Utot 312420
4113 Utot 320502
4114 Utot 279053
4115 Utot 280480
4116 Utot 317143
4117 Utot 335443
4118 Utot 304483
4119 Utot 299670
4120 Utot 391082
4121 Utot 322888
4122 Utot 343419
4123 Utot 335820
4124 Utot 337171
4125 Utot 357039
4126 Utot 293349
4127 Utot 322200
4128 Utot 321135
4129 Utot 329483
4130 Utot 320537
4131 Utot 278861
4132 Utot 296395
4133 Utot 371891
4134 Utot 306420
4135 Utot 300436
4136 Utot 304609
4137 Utot 381946
4138 Utot 300274
4139 Utot 371335
4140 Utot 345040
4141 Utot 310855
4142 Utot 299477
4143 Utot 271283
4144 Utot 324254
4145 Utot 339245
4146 Utot 283502
4147 Utot 378853
4148 Utot 388392
4149 Utot 308234
4150 Utot 285566
4151 Utot 330996
4152 Utot 349263
4153 Utot 350320
4154 Utot 343619
4155 Utot 326563
4156 Utot 317641
4157 Utot 334619
4158 Utot 328537
4159 Utot 321407
4160 Utot 283601
4161 Utot 350679
4162 Utot 336616
4163 Utot 315801
4164 Utot 299433
4165 Utot 288513
4166 Utot 350246
4167 Utot 396992
4168 Utot 287576
4169 Utot 369461
4170 Utot 315622
4171 Utot 297742
4172 Utot 286255
4173 Utot 335053
4174 Utot 351558
4175 Utot 316650
4176 Utot 390424
4177 Utot 367441
4178 Utot 341444
4179 Utot 292415
4180 Utot 322791
4181 Utot 355850
4182 Utot 381713
4183 Utot 291271
4184 Utot 317856
4185 Utot 349888
4186 Utot 366977
4187 Utot 393226
4188 Utot 333661
4189 Utot 312977
4190 Utot 333271
4191 Utot 334336
4192 Utot 299047
4193 Utot 319598
4194 Utot 309240
4195 Utot 326695
4196 Utot 300915
4197 Utot 326107
4198 Utot 295911
4199 Utot 316146
4200 Utot 392277
4201 Utot 347889
4202 Utot 293556
4203 Utot 349063
4204 Utot 343929
4205 Utot 383196
4206 Utot 346945
4207 Utot 365138
4208 Utot 365112
4209 Utot 325862
4210 Utot 305392
4211 Utot 300356
4212 Utot 294615
4213 Utot 360131
4214 Utot 346160
4215 Utot 300941
4216 Utot 349893
4217 Utot 318093
4218 Utot 408603
4219 Utot 377774
4220 Utot 381281
4221 Utot 286414
4222 Utot 292646
4223 Utot 322696
4224 Utot 295908
4225 Utot 309068
4226 Utot 277827
4227 Utot 338986
4228 Utot 336339
4229 Utot 396936
4230 Utot 396568
4231 Utot 345665
4232 Utot 317698
4233 Utot 314867
4234 Utot 298715
4235 Utot 319058
4236 Utot 345928
4237 Utot 357468
4238 Utot 312411
4239 Utot 300240
4240 Utot 398050
4241 Utot 353652
4242 Utot 343973
4243 Utot 336476
4244 Utot 337267
4245 Utot 295404
4246 Utot 319513
4247 Utot 292226
4248 Utot 339883
4249 Utot 314618
4250 Utot 336749
4251 Utot 348327
4252 Utot 283332
4253 Utot 337294
4254 Utot 304721
4255 Utot 342657
4256 Utot 314895
4257 Utot 380218
4258 Utot 323504
4259 Utot 301185
4260 Utot 362877
4261 Utot 299461
4262 Utot 322918
4263 Utot 304963
4264 Utot 289052
4265 Utot 317534
4266 Utot 391769
4267 Utot 347494
4268 Utot 369647
4269 Utot 348785
4270 Utot 369352
4271 Utot 338301
4272 Utot 312025
4273 Utot 347791
4274 Utot 341127
4275 Utot 338236
4276 Utot 316126
4277 Utot 300982
4278 Utot 310734
4279 Utot 351281
4280 Utot 369082
4281 Utot 310314
4282 Utot 317992
4283 Utot 310137
4284 Utot 322275
4285 Utot 339982
4286 Utot 400419
4287 Utot 354064
4288 Utot 288211
4289 Utot 376047
4290 Utot 326226
4291 Utot 325894
4292 Utot 327255
4293 Utot 333460
4294 Utot 406600
4295 Utot 343837
4296 Utot 364909
4297 Utot 323076
4298 Utot 409630
4299 Utot 290006
4300 Utot 335972
4301 Utot 407474
4302 Utot 305847
4303 Utot 291940
4304 Utot 335235
4305 Utot 359965
4306 Utot 354282
4307 Utot 341303
4308 Utot 340496
4309 Utot 409582
4310 Utot 313966
4311 Utot 327435
4312 Utot 335516
4313 Utot 270392
4314 Utot 365573
4315 Utot 356642
4316 Utot 435457
4317 Utot 363238
4318 Utot 299934
4319 Utot 314334
4320 Utot 334817
4321 Utot 370880
4322 Utot 376260
4323 Utot 375416
4324 Utot 288419
4325 Utot 297369
4326 Utot 325253
4327 Utot 307522
4328 Utot 333760
4329 Utot 357080
4330 Utot 363226
4331 Utot 331668
4332 Utot 291732
4333 Utot 318841
4334 Utot 301969
4335 Utot 316528
4336 Utot 321979
4337 Utot 330857
4338 Utot 275680
4339 Utot 334096
4340 Utot 421074
4341 Utot 361450
4342 Utot 299653
4343 Utot 306351
4344 Utot 384808
4345 Utot 491686
4346 Utot 315537
4347 Utot 374372
4348 Utot 340073
4349 Utot 346555
4350 Utot 279052
4351 Utot 349494
4352 Utot 303019
4353 Utot 387574
4354 Utot 294883
4355 Utot 312373
4356 Utot 353484
4357 Utot 389592
4358 Utot 293070
4359 Utot 415813
4360 Utot 290618
4361 Utot 320722
4362 Utot 283334
4363 Utot 304530
4364 Utot 310048
4365 Utot 324066
4366 Utot 304019
4367 Utot 275250
4368 Utot 300872
4369 Utot 373382
4370 Utot 302083
4371 Utot 374300
4372 Utot 270885
4373 Utot 330325
4374 Utot 325703
4375 Utot 389357
4376 Utot 297233
4377 Utot 368817
4378 Utot 331733
4379 Utot 367418
4380 Utot 327603
4381 Utot 348717
4382 Utot 311821
4383 Utot 363904
4384 Utot 383259
4385 Utot 372151
4386 Utot 328548
4387 Utot 304069
4388 Utot 285561
4389 Utot 287325
4390 Utot 324129
4391 Utot 317587
4392 Utot 296902
4393 Utot 299314
4394 Utot 414337
4395 Utot 345175
4396 Utot 333388
4397 Utot 307417
4398 Utot 276554
4399 Utot 324348
4400 Utot 304017
4401 Utot 291465
4402 Utot 307111
4403 Utot 327246
4404 Utot 301868
4405 Utot 333470
4406 Utot 295765
4407 Utot 353233
4408 Utot 395190
4409 Utot 303389
4410 Utot 359349
4411 Utot 374163
4412 Utot 337989
4413 Utot 306283
4414 Utot 309859
4415 Utot 303242
4416 Utot 305291
4417 Utot 297805
4418 Utot 306291
4419 Utot 323168
4420 Utot 370314
4421 Utot 277379
4422 Utot 339437
4423 Utot 303457
4424 Utot 327791
4425 Utot 384897
4426 Utot 301780
4427 Utot 358419
4428 Utot 283578
4429 Utot 347153
4430 Utot 329124
4431 Utot 347776
4432 Utot 323384
4433 Utot 288983
4434 Utot 302476
4435 Utot 335813
4436 Utot 290968
4437 Utot 296752
4438 Utot 319034
4439 Utot 316595
4440 Utot 324994
4441 Utot 334581
4442 Utot 341005
4443 Utot 320431
4444 Utot 376555
4445 Utot 289089
4446 Utot 382144
4447 Utot 301044
4448 Utot 377419
4449 Utot 293335
4450 Utot 363796
4451 Utot 307394
4452 Utot 297006
4453 Utot 297833
4454 Utot 277465
4455 Utot 287507
4456 Utot 351841
4457 Utot 310124
4458 Utot 285655
4459 Utot 287526
4460 Utot 346665
4461 Utot 296193
4462 Utot 336076
4463 Utot 327852
4464 Utot 310775
4465 Utot 295341
4466 Utot 363939
4467 Utot 338397
4468 Utot 357301
4469 Utot 312577
4470 Utot 321795
4471 Utot 314022
4472 Utot 301699
4473 Utot 351810
4474 Utot 321051
4475 Utot 404670
4476 Utot 433685
4477 Utot 277913
4478 Utot 317668
4479 Utot 394612
4480 Utot 335706
4481 Utot 351673
4482 Utot 365959
4483 Utot 375599
4484 Utot 385994
4485 Utot 317233
4486 Utot 305485
4487 Utot 300754
4488 Utot 332398
4489 Utot 334354
4490 Utot 385966
4491 Utot 300512
4492 Utot 336653
4493 Utot 307449
4494 Utot 327144
4495 Utot 342651
4496 Utot 335039
4497 Utot 357227
4498 Utot 297840
4499 Utot 387801
4500 Utot 332766
4501 Utot 369527
4502 Utot 323197
4503 Utot 362512
4504 Utot 325044
4505 Utot 350146
4506 Utot 310703
4507 Utot 310814
4508 Utot 326773
4509 Utot 388196
4510 Utot 317693
4511 Utot 311118
4512 Utot 355448
4513 Utot 325407
4514 Utot 396008
4515 Utot 321466
4516 Utot 320678
4517 Utot 311818
4518 Utot 285139
4519 Utot 269387
4520 Utot 352420
4521 Utot 360104
4522 Utot 349329
4523 Utot 299509
4524 Utot 313606
4525 Utot 313568
4526 Utot 345842
4527 Utot 341890
4528 Utot 291662
4529 Utot 297651
4530 Utot 342872
4531 Utot 308667
4532 Utot 311685
4533 Utot 431737
4534 Utot 298892
4535 Utot 338175
4536 Utot 337385
4537 Utot 349333
4538 Utot 337186
4539 Utot 376022
4540 Utot 296684
4541 Utot 337398
4542 Utot 307413
4543 Utot 340376
4544 Utot 325000
4545 Utot 325609
4546 Utot 328427
4547 Utot 310318
4548 Utot 304150
4549 Utot 353804
4550 Utot 354522
4551 Utot 318884
4552 Utot 408743
4553 Utot 337006
4554 Utot 340480
4555 Utot 354406
4556 Utot 354136
4557 Utot 329138
4558 Utot 352090
4559 Utot 321557
4560 Utot 399768
4561 Utot 349533
4562 Utot 352613
4563 Utot 313137
4564 Utot 288987
4565 Utot 287730
4566 Utot 324080
4567 Utot 358246
4568 Utot 332403
4569 Utot 348645
4570 Utot 309434
4571 Utot 298403
4572 Utot 313370
4573 Utot 339776
4574 Utot 323996
4575 Utot 311472
4576 Utot 296726
4577 Utot 398287
4578 Utot 350900
4579 Utot 317040
4580 Utot 366209
4581 Utot 272486
4582 Utot 359157
4583 Utot 314301
4584 Utot 353349
4585 Utot 340361
4586 Utot 288147
4587 Utot 320938
4588 Utot 330807
4589 Utot 303047
4590 Utot 309295
4591 Utot 281967
4592 Utot 315254
4593 Utot 311340
4594 Utot 310221
4595 Utot 305451
4596 Utot 368466
4597 Utot 309387
4598 Utot 313834
4599 Utot 334359
4600 Utot 482422
4601 Utot 418944
4602 Utot 378933
4603 Utot 379659
4604 Utot 350595
4605 Utot 288694
4606 Utot 347653
4607 Utot 374596
4608 Utot 362381
4609 Utot 308415
4610 Utot 308078
4611 Utot 312334
4612 Utot 439375
4613 Utot 309252
4614 Utot 276795
4615 Utot 342188
4616 Utot 385855
4617 Utot 350628
4618 Utot 307932
4619 Utot 429431
4620 Utot 346385
4621 Utot 343478
4622 Utot 338645
4623 Utot 386522
4624 Utot 287049
4625 Utot 371993
4626 Utot 344964
4627 Utot 326475
4628 Utot 283019
4629 Utot 309148
4630 Utot 350678
4631 Utot 362891
4632 Utot 362228
4633 Utot 297245
4634 Utot 403649
4635 Utot 351908
4636 Utot 306090
4637 Utot 330758
4638 Utot 321602
4639 Utot 412554
4640 Utot 310207
4641 Utot 321932
4642 Utot 304624
4643 Utot 304235
4644 Utot 303118
4645 Utot 277448
4646 Utot 358474
4647 Utot 325141
4648 Utot 288284
4649 Utot 341697
4650 Utot 333747
4651 Utot 347359
4652 Utot 341079
4653 Utot 321479
4654 Utot 305714
4655 Utot 326165
4656 Utot 355457
4657 Utot 348118
4658 Utot 342933
4659 Utot 304029
4660 Utot 322996
4661 Utot 344500
4662 Utot 288004
4663 Utot 360069
4664 Utot 328502
4665 Utot 349753
4666 Utot 294333
4667 Utot 341209
4668 Utot 306004
4669 Utot 310616
4670 Utot 273328
4671 Utot 377467
4672 Utot 312733
4673 Utot 356758
4674 Utot 297048
4675 Utot 293767
4676 Utot 331749
4677 Utot 303497
4678 Utot 319438
4679 Utot 314840
4680 Utot 323942
4681 Utot 303943
4682 Utot 309156
4683 Utot 395225
4684 Utot 318271
4685 Utot 341406
4686 Utot 323499
4687 Utot 355577
4688 Utot 284246
4689 Utot 318004
4690 Utot 531650
4691 Utot 317232
4692 Utot 330485
4693 Utot 365240
4694 Utot 317173
4695 Utot 317247
4696 Utot 301197
4697 Utot 319992
4698 Utot 310669
4699 Utot 353616
4700 Utot 286057
4701 Utot 333180
4702 Utot 354658
4703 Utot 350569
4704 Utot 399930
4705 Utot 425114
4706 Utot 350893
4707 Utot 326675
4708 Utot 291227
4709 Utot 302924
4710 Utot 288660
4711 Utot 314038
4712 Utot 355219
4713 Utot 329935
4714 Utot 298501
4715 Utot 333282
4716 Utot 289096
4717 Utot 335544
4718 Utot 364563
4719 Utot 331398
4720 Utot 387442
4721 Utot 329339
4722 Utot 308977
4723 Utot 331906
4724 Utot 344165
4725 Utot 344302
4726 Utot 258212
4727 Utot 305643
4728 Utot 301224
4729 Utot 286710
4730 Utot 351040
4731 Utot 311159
4732 Utot 322179
4733 Utot 267184
4734 Utot 312279
4735 Utot 358488
4736 Utot 277816
4737 Utot 321982
4738 Utot 338329
4739 Utot 326450
4740 Utot 356450
4741 Utot 323313
4742 Utot 298795
4743 Utot 333257
4744 Utot 372440
4745 Utot 343593
4746 Utot 308027
4747 Utot 379580
4748 Utot 301414
4749 Utot 379186
4750 Utot 380246
4751 Utot 379891
4752 Utot 349734
4753 Utot 335523
4754 Utot 360059
4755 Utot 316868
4756 Utot 284420
4757 Utot 397729
4758 Utot 347053
4759 Utot 330636
4760 Utot 383314
4761 Utot 339826
4762 Utot 320930
4763 Utot 321955
4764 Utot 327738
4765 Utot 332831
4766 Utot 289712
4767 Utot 340964
4768 Utot 312505
4769 Utot 355681
4770 Utot 380971
4771 Utot 342538
4772 Utot 329096
4773 Utot 315439
4774 Utot 335231
4775 Utot 261982
4776 Utot 321523
4777 Utot 372489
4778 Utot 290427
4779 Utot 343557
4780 Utot 286171
4781 Utot 370594
4782 Utot 313610
4783 Utot 303898
4784 Utot 319235
4785 Utot 378689
4786 Utot 312540
4787 Utot 369341
4788 Utot 311874
4789 Utot 303199
4790 Utot 309943
4791 Utot 387636
4792 Utot 368033
4793 Utot 318252
4794 Utot 316045
4795 Utot 348378
4796 Utot 353164
4797 Utot 294163
4798 Utot 335978
4799 Utot 316035
4800 Utot 276874
4801 Utot 339500
4802 Utot 298708
4803 Utot 305347
4804 Utot 356114
4805 Utot 320397
4806 Utot 359144
4807 Utot 325949
4808 Utot 328058
4809 Utot 313206
4810 Utot 334392
4811 Utot 306712
4812 Utot 328946
4813 Utot 422009
4814 Utot 341855
4815 Utot 322058
4816 Utot 310476
4817 Utot 346806
4818 Utot 339557
4819 Utot 359327
4820 Utot 371199
4821 Utot 352317
4822 Utot 268555
4823 Utot 360213
4824 Utot 271691
4825 Utot 323097
4826 Utot 333862
4827 Utot 328684
4828 Utot 337065
4829 Utot 317697
4830 Utot 279510
4831 Utot 345535
4832 Utot 381042
4833 Utot 381288
4834 Utot 324548
4835 Utot 309344
4836 Utot 336196
4837 Utot 316445
4838 Utot 415049
4839 Utot 267743
4840 Utot 310987
4841 Utot 329454
4842 Utot 332965
4843 Utot 321883
4844 Utot 287800
4845 Utot 297456
4846 Utot 305771
4847 Utot 339178
4848 Utot 331808
4849 Utot 309308
4850 Utot 309394
4851 Utot 303350
4852 Utot 352351
4853 Utot 384560
4854 Utot 332504
4855 Utot 291269
4856 Utot 327207
4857 Utot 350007
4858 Utot 322728
4859 Utot 321677
4860 Utot 298849
4861 Utot 283178
4862 Utot 339045
4863 Utot 300002
4864 Utot 290841
4865 Utot 344667
4866 Utot 350846
4867 Utot 314446
4868 Utot 326935
4869 Utot 365892
4870 Utot 293008
4871 Utot 327843
4872 Utot 367301
4873 Utot 354863
4874 Utot 414318
4875 Utot 312339
4876 Utot 336358
4877 Utot 323797
4878 Utot 314656
4879 Utot 418745
4880 Utot 278793
4881 Utot 348513
4882 Utot 344558
4883 Utot 308421
4884 Utot 330632
4885 Utot 303139
4886 Utot 333747
4887 Utot 308333
4888 Utot 316962
4889 Utot 370712
4890 Utot 307243
4891 Utot 373695
4892 Utot 296909
4893 Utot 287272
4894 Utot 311104
4895 Utot 307523
4896 Utot 316638
4897 Utot 288836
4898 Utot 303706
4899 Utot 295231
4900 Utot 317389
4901 Utot 344049
4902 Utot 354845
4903 Utot 330890
4904 Utot 344689
4905 Utot 430064
4906 Utot 321525
4907 Utot 298745
4908 Utot 331508
4909 Utot 312687
4910 Utot 315019
4911 Utot 307334
4912 Utot 282819
4913 Utot 374261
4914 Utot 317247
4915 Utot 308109
4916 Utot 402934
4917 Utot 315908
4918 Utot 404126
4919 Utot 307858
4920 Utot 324004
4921 Utot 323057
4922 Utot 352573
4923 Utot 338636
4924 Utot 398861
4925 Utot 295132
4926 Utot 317696
4927 Utot 319995
4928 Utot 403520
4929 Utot 385366
4930 Utot 313225
4931 Utot 342600
4932 Utot 346908
4933 Utot 299258
4934 Utot 369342
4935 Utot 285161
4936 Utot 379037
4937 Utot 286158
4938 Utot 382145
4939 Utot 299881
4940 Utot 283821
4941 Utot 315964
4942 Utot 334896
4943 Utot 301990
4944 Utot 391523
4945 Utot 366070
4946 Utot 293920
4947 Utot 310426
4948 Utot 344152
4949 Utot 284610
4950 Utot 351674
4951 Utot 357216
4952 Utot 280719
4953 Utot 294114
4954 Utot 314118
4955 Utot 286721
4956 Utot 334686
4957 Utot 309443
4958 Utot 358198
4959 Utot 294786
4960 Utot 302961
4961 Utot 310301
4962 Utot 299733
4963 Utot 304978
4964 Utot 307943
4965 Utot 337864
4966 Utot 332473
4967 Utot 286807
4968 Utot 395050
4969 Utot 379443
4970 Utot 307047
4971 Utot 336115
4972 Utot 310569
4973 Utot 403848
4974 Utot 437853
4975 Utot 329901
4976 Utot 301386
4977 Utot 396975
4978 Utot 436951
4979 Utot 292054
4980 Utot 352964
4981 Utot 375196
4982 Utot 334095
4983 Utot 359041
4984 Utot 308853
4985 Utot 282272
4986 Utot 298715
4987 Utot 318503
4988 Utot 312953
4989 Utot 306595
4990 Utot 321196
4991 Utot 344695
4992 Utot 336009
4993 Utot 339073
4994 Utot 324348
4995 Utot 377031
4996 Utot 398937
4997 Utot 318986
4998 Utot 325407
4999 Utot 317193
5000 Utot 318075
5001 Utot 418278
5002 Utot 321835
5003 Utot 384411
5004 Utot 345399
5005 Utot 288506
5006 Utot 302236
5007 Utot 317342
5008 Utot 371791
5009 Utot 281966
5010 Utot 325114
5011 Utot 352674
5012 Utot 306917
5013 Utot 344602
5014 Utot 316220
5015 Utot 323170
5016 Utot 308837
5017 Utot 306924
5018 Utot 341248
5019 Utot 335467
5020 Utot 308891
5021 Utot 321200
5022 Utot 369773
5023 Utot 309685
5024 Utot 317177
5025 Utot 311311
5026 Utot 287324
5027 Utot 290952
5028 Utot 348872
5029 Utot 321895
5030 Utot 323675
5031 Utot 323782
5032 Utot 353224
5033 Utot 321763
5034 Utot 282365
5035 Utot 385522
5036 Utot 307112
5037 Utot 326512
5038 Utot 346617
5039 Utot 295820
5040 Utot 364695
5041 Utot 369167
5042 Utot 333924
5043 Utot 450902
5044 Utot 346127
5045 Utot 309516
5046 Utot 373196
5047 Utot 326770
5048 Utot 385171
5049 Utot 294645
5050 Utot 356133
5051 Utot 308485
5052 Utot 343639
5053 Utot 344448
5054 Utot 373497
5055 Utot 321190
5056 Utot 318184
5057 Utot 308966
5058 Utot 292944
5059 Utot 359232
5060 Utot 326602
5061 Utot 293236
5062 Utot 308197
5063 Utot 321879
5064 Utot 286950
5065 Utot 314108
5066 Utot 341138
5067 Utot 335342
5068 Utot 342348
5069 Utot 374332
5070 Utot 356779
5071 Utot 301277
5072 Utot 344100
5073 Utot 338235
5074 Utot 359921
5075 Utot 305569
5076 Utot 305802
5077 Utot 313366
5078 Utot 372913
5079 Utot 309933
5080 Utot 395100
5081 Utot 357751
5082 Utot 308668
5083 Utot 362357
5084 Utot 293481
5085 Utot 333654
5086 Utot 344688
5087 Utot 364036
5088 Utot 330493
5089 Utot 337524
5090 Utot 315847
5091 Utot 309933
5092 Utot 358409
5093 Utot 301539
5094 Utot 332751
5095 Utot 384509
5096 Utot 311679
5097 Utot 320981
5098 Utot 333004
5099 Utot 378325
5100 Utot 331539
5101 Utot 327473
5102 Utot 386770
5103 Utot 314071
5104 Utot 308874
5105 Utot 315400
5106 Utot 312991
5107 Utot 286404
5108 Utot 322394
5109 Utot 346367
5110 Utot 305535
5111 Utot 334286
5112 Utot 345774
5113 Utot 329300
5114 Utot 368850
5115 Utot 364635
5116 Utot 346538
5117 Utot 333814
5118 Utot 322053
5119 Utot 327054
5120 Utot 337500
5121 Utot 341079
5122 Utot 326913
5123 Utot 356613
5124 Utot 316037
5125 Utot 346060
5126 Utot 383330
5127 Utot 334802
5128 Utot 332979
5129 Utot 331271
5130 Utot 333577
5131 Utot 402626
5132 Utot 304966
5133 Utot 360070
5134 Utot 344765
5135 Utot 289338
5136 Utot 332089
5137 Utot 346266
5138 Utot 321094
5139 Utot 399873
5140 Utot 341469
5141 Utot 315468
5142 Utot 352643
5143 Utot 344279
5144 Utot 339729
5145 Utot 323373
5146 Utot 308313
5147 Utot 356553
5148 Utot 318828
5149 Utot 333987
5150 Utot 310419
5151 Utot 277552
5152 Utot 399765
5153 Utot 369233
5154 Utot 347190
5155 Utot 327696
5156 Utot 286261
5157 Utot 291816
5158 Utot 334136
5159 Utot 346861
5160 Utot 319431
5161 Utot 303031
5162 Utot 329030
5163 Utot 328944
5164 Utot 335289
5165 Utot 336891
5166 Utot 395786
5167 Utot 282069
5168 Utot 322783
5169 Utot 332505
5170 Utot 317464
5171 Utot 321250
5172 Utot 348705
5173 Utot 435947
5174 Utot 376064
5175 Utot 298264
5176 Utot 325676
5177 Utot 338080
5178 Utot 289664
5179 Utot 286709
5180 Utot 318181
5181 Utot 328802
5182 Utot 308117
5183 Utot 321113
5184 Utot 376627
5185 Utot 389641
5186 Utot 327017
5187 Utot 312371
5188 Utot 364682
5189 Utot 316671
5190 Utot 306189
5191 Utot 387585
5192 Utot 300069
5193 Utot 296067
5194 Utot 410599
5195 Utot 281821
5196 Utot 390608
5197 Utot 342460
5198 Utot 292222
5199 Utot 329734
5200 Utot 365211
5201 Utot 317017
5202 Utot 361680
5203 Utot 323858
5204 Utot 314270
5205 Utot 363862
5206 Utot 337296
5207 Utot 343841
5208 Utot 358313
5209 Utot 378601
5210 Utot 313615
5211 Utot 371900
5212 Utot 279738
5213 Utot 363926
5214 Utot 290911
5215 Utot 302490
5216 Utot 340347
5217 Utot 292592
5218 Utot 332754
5219 Utot 356021
5220 Utot 346820
5221 Utot 357260
5222 Utot 314799
5223 Utot 334994
5224 Utot 296166
5225 Utot 288254
5226 Utot 352149
5227 Utot 294737
5228 Utot 354111
5229 Utot 315327
5230 Utot 352583
5231 Utot 315666
5232 Utot 270157
5233 Utot 347424
5234 Utot 361377
5235 Utot 348978
5236 Utot 327523
5237 Utot 291389
5238 Utot 449914
5239 Utot 298318
5240 Utot 377130
5241 Utot 300944
5242 Utot 373219
5243 Utot 305820
5244 Utot 413906
5245 Utot 358422
5246 Utot 344342
5247 Utot 396856
5248 Utot 305597
5249 Utot 287569
5250 Utot 313168
5251 Utot 364150
5252 Utot 324875
5253 Utot 332511
5254 Utot 358274
5255 Utot 303223
5256 Utot 321540
5257 Utot 343556
5258 Utot 332200
5259 Utot 317731
5260 Utot 331689
5261 Utot 368587
5262 Utot 340016
5263 Utot 340734
5264 Utot 323291
5265 Utot 337392
5266 Utot 331440
5267 Utot 402207
5268 Utot 320937
5269 Utot 296423
5270 Utot 323344
5271 Utot 313740
5272 Utot 305001
5273 Utot 462122
5274 Utot 355325
5275 Utot 310943
5276 Utot 369497
5277 Utot 339768
5278 Utot 338059
5279 Utot 354432
5280 Utot 302141
5281 Utot 380144
5282 Utot 288312
5283 Utot 329561
5284 Utot 343160
5285 Utot 316246
5286 Utot 319155
5287 Utot 339396
5288 Utot 340651
5289 Utot 374375
5290 Utot 282548
5291 Utot 319215
5292 Utot 314533
5293 Utot 305876
5294 Utot 319906
5295 Utot 295471
5296 Utot 328159
5297 Utot 290373
5298 Utot 315016
5299 Utot 323482
5300 Utot 392769
5301 Utot 355292
5302 Utot 342562
5303 Utot 349577
5304 Utot 389880
5305 Utot 306389
5306 Utot 360326
5307 Utot 349145
5308 Utot 329382
5309 Utot 314604
5310 Utot 309856
5311 Utot 346602
5312 Utot 282758
5313 Utot 357365
5314 Utot 311388
5315 Utot 345578
5316 Utot 314976
5317 Utot 317666
5318 Utot 329926
5319 Utot 308119
5320 Utot 305496
5321 Utot 280264
5322 Utot 319833
5323 Utot 357976
5324 Utot 348992
5325 Utot 286507
5326 Utot 296203
5327 Utot 329073
5328 Utot 278490
5329 Utot 299028
5330 Utot 298615
5331 Utot 376300
5332 Utot 324887
5333 Utot 315277
5334 Utot 402647
5335 Utot 407593
5336 Utot 384344
5337 Utot 289502
5338 Utot 430228
5339 Utot 333226
5340 Utot 302663
5341 Utot 365908
5342 Utot 345180
5343 Utot 296196
5344 Utot 311621
5345 Utot 312958
5346 Utot 412837
5347 Utot 353352
5348 Utot 368363
5349 Utot 348131
5350 Utot 333134
5351 Utot 296215
5352 Utot 397040
5353 Utot 335967
5354 Utot 306587
5355 Utot 292307
5356 Utot 295353
5357 Utot 270676
5358 Utot 334962
5359 Utot 350739
5360 Utot 324201
5361 Utot 351247
5362 Utot 313407
5363 Utot 347992
5364 Utot 338100
5365 Utot 282119
5366 Utot 346279
5367 Utot 358802
5368 Utot 421002
5369 Utot 327568
5370 Utot 289578
5371 Utot 313569
5372 Utot 378779
5373 Utot 335684
5374 Utot 343737
5375 Utot 346099
5376 Utot 332426
5377 Utot 298826
5378 Utot 340977
5379 Utot 294449
5380 Utot 323671
5381 Utot 278516
5382 Utot 292009
5383 Utot 358089
5384 Utot 328832
5385 Utot 305061
5386 Utot 349175
5387 Utot 356162
5388 Utot 349814
5389 Utot 392602
5390 Utot 315131
5391 Utot 311193
5392 Utot 335819
5393 Utot 297489
5394 Utot 309576
5395 Utot 306905
5396 Utot 279951
5397 Utot 332199
5398 Utot 334383
5399 Utot 336345
5400 Utot 391864
5401 Utot 301331
5402 Utot 306812
5403 Utot 381924
5404 Utot 350117
5405 Utot 291659
5406 Utot 335862
5407 Utot 321476
5408 Utot 362278
5409 Utot 307770
5410 Utot 303412
5411 Utot 298910
5412 Utot 375713
5413 Utot 356109
5414 Utot 289565
5415 Utot 407886
5416 Utot 309671
5417 Utot 322054
5418 Utot 297695
5419 Utot 338942
5420 Utot 289700
5421 Utot 283957
5422 Utot 310127
5423 Utot 337091
5424 Utot 421079
5425 Utot 314154
5426 Utot 320700
5427 Utot 372045
5428 Utot 324459
5429 Utot 367452
5430 Utot 269663
5431 Utot 299264
5432 Utot 282425
5433 Utot 315710
5434 Utot 372367
5435 Utot 323018
5436 Utot 309824
5437 Utot 357377
5438 Utot 400601
5439 Utot 401330
5440 Utot 285714
5441 Utot 303161
5442 Utot 313498
5443 Utot 309566
5444 Utot 336464
5445 Utot 314202
5446 Utot 266005
5447 Utot 299141
5448 Utot 293907
5449 Utot 348422
5450 Utot 340725
5451 Utot 385389
5452 Utot 375305
5453 Utot 378671
5454 Utot 309183
5455 Utot 317472
5456 Utot 374212
5457 Utot 340546
5458 Utot 338211
5459 Utot 362867
5460 Utot 358288
5461 Utot 348260
5462 Utot 295163
5463 Utot 368080
5464 Utot 375807
5465 Utot 348847
5466 Utot 301035
5467 Utot 296803
5468 Utot 347086
5469 Utot 397406
5470 Utot 326030
5471 Utot 365311
5472 Utot 303447
5473 Utot 312321
5474 Utot 363683
5475 Utot 288374
5476 Utot 358572
5477 Utot 323518
5478 Utot 332783
5479 Utot 412579
5480 Utot 352941
5481 Utot 318784
5482 Utot 337425
5483 Utot 327767
5484 Utot 350121
5485 Utot 330091
5486 Utot 334888
5487 Utot 306118
5488 Utot 368983
5489 Utot 334389
5490 Utot 299685
5491 Utot 345343
5492 Utot 304860
5493 Utot 327420
5494 Utot 328161
5495 Utot 320981
5496 Utot 310936
5497 Utot 400840
5498 Utot 314568
5499 Utot 322825
5500 Utot 312339
5501 Utot 333083
5502 Utot 307394
5503 Utot 379540
5504 Utot 327265
5505 Utot 383135
5506 Utot 341963
5507 Utot 387032
5508 Utot 306833
5509 Utot 353010
5510 Utot 335212
5511 Utot 354698
5512 Utot 287515
5513 Utot 313738
5514 Utot 328940
5515 Utot 309783
5516 Utot 309162
5517 Utot 275476
5518 Utot 328096
5519 Utot 306040
5520 Utot 295136
5521 Utot 396304
5522 Utot 291151
5523 Utot 332648
5524 Utot 404790
5525 Utot 298409
5526 Utot 351207
5527 Utot 341218
5528 Utot 333278
5529 Utot 390497
5530 Utot 353129
5531 Utot 300442
5532 Utot 315095
5533 Utot 404842
5534 Utot 322446
5535 Utot 326491
5536 Utot 316188
5537 Utot 291910
5538 Utot 336118
5539 Utot 329505
5540 Utot 334325
5541 Utot 331310
5542 Utot 381782
5543 Utot 324314
5544 Utot 366884
5545 Utot 336795
5546 Utot 375940
5547 Utot 311900
5548 Utot 324864
5549 Utot 374744
5550 Utot 302706
5551 Utot 298383
5552 Utot 285776
5553 Utot 326567
5554 Utot 294292
5555 Utot 297063
5556 Utot 323935
5557 Utot 323599
5558 Utot 334508
5559 Utot 410987
5560 Utot 369344
5561 Utot 313808
5562 Utot 321855
5563 Utot 288948
5564 Utot 376131
5565 Utot 329421
5566 Utot 304724
5567 Utot 374204
5568 Utot 365174
5569 Utot 349446
5570 Utot 364105
5571 Utot 341214
5572 Utot 328576
5573 Utot 321293
5574 Utot 418578
5575 Utot 317325
5576 Utot 387773
5577 Utot 316469
5578 Utot 343845
5579 Utot 394396
5580 Utot 278213
5581 Utot 306494
5582 Utot 344125
5583 Utot 285755
5584 Utot 347439
5585 Utot 346419
5586 Utot 321088
5587 Utot 298144
5588 Utot 305987
5589 Utot 362620
5590 Utot 350815
5591 Utot 329688
5592 Utot 313372
5593 Utot 349257
5594 Utot 353890
5595 Utot 351585
5596 Utot 356664
5597 Utot 317099
5598 Utot 300340
5599 Utot 339674
5600 Utot 352611
5601 Utot 282197
5602 Utot 409533
5603 Utot 317468
5604 Utot 307392
5605 Utot 368952
5606 Utot 361028
5607 Utot 327857
5608 Utot 286035
5609 Utot 295813
5610 Utot 336578
5611 Utot 291706
5612 Utot 330887
5613 Utot 378104
5614 Utot 317316
5615 Utot 342244
5616 Utot 322132
5617 Utot 457062
5618 Utot 345286
5619 Utot 299617
5620 Utot 361124
5621 Utot 312136
5622 Utot 321675
5623 Utot 302117
5624 Utot 354393
5625 Utot 396749
5626 Utot 318151
5627 Utot 283594
5628 Utot 373626
5629 Utot 328304
5630 Utot 314173
5631 Utot 298200
5632 Utot 359753
5633 Utot 332281
5634 Utot 404224
5635 Utot 308766
5636 Utot 322496
5637 Utot 418974
5638 Utot 345888
5639 Utot 301095
5640 Utot 315679
5641 Utot 367029
5642 Utot 350180
5643 Utot 304312
5644 Utot 375997
5645 Utot 295779
5646 Utot 295351
5647 Utot 299664
5648 Utot 336019
5649 Utot 387039
5650 Utot 279076
5651 Utot 381885
5652 Utot 327165
5653 Utot 348983
5654 Utot 319029
5655 Utot 297003
5656 Utot 297000
5657 Utot 285456
5658 Utot 342334
5659 Utot 297729
5660 Utot 337847
5661 Utot 358015
5662 Utot 341087
5663 Utot 293654
5664 Utot 282535
5665 Utot 347773
5666 Utot 366006
5667 Utot 291883
5668 Utot 312197
5669 Utot 390969
5670 Utot 289464
5671 Utot 351995
5672 Utot 319446
5673 Utot 308939
5674 Utot 340725
5675 Utot 364904
5676 Utot 415862
5677 Utot 277606
5678 Utot 304145
5679 Utot 345153
5680 Utot 282744
5681 Utot 353244
5682 Utot 301712
5683 Utot 332691
5684 Utot 277340
5685 Utot 357606
5686 Utot 361077
5687 Utot 335455
5688 Utot 346366
5689 Utot 348091
5690 Utot 299888
5691 Utot 327399
5692 Utot 307782
5693 Utot 379059
5694 Utot 308591
5695 Utot 263565
5696 Utot 326581
5697 Utot 336783
5698 Utot 308398
5699 Utot 364647
5700 Utot 301136
5701 Utot 311208
5702 Utot 309664
5703 Utot 351370
5704 Utot 306945
5705 Utot 338763
5706 Utot 274402
5707 Utot 327736
5708 Utot 428623
5709 Utot 309208
5710 Utot 296530
5711 Utot 325133
5712 Utot 374526
5713 Utot 299108
5714 Utot 346893
5715 Utot 321160
5716 Utot 321009
5717 Utot 339424
5718 Utot 295571
5719 Utot 315327
5720 Utot 315485
5721 Utot 314789
5722 Utot 298582
5723 Utot 322764
5724 Utot 331320
5725 Utot 336118
5726 Utot 313004
5727 Utot 300648
5728 Utot 328118
5729 Utot 337052
5730 Utot 339149
5731 Utot 307660
5732 Utot 313415
5733 Utot 372393
5734 Utot 321849
5735 Utot 329744
5736 Utot 324757
5737 Utot 344382
5738 Utot 356390
5739 Utot 311404
5740 Utot 367812
5741 Utot 304776
5742 Utot 330163
5743 Utot 283588
5744 Utot 326168
5745 Utot 330768
5746 Utot 278633
5747 Utot 319783
5748 Utot 388017
5749 Utot 315121
5750 Utot 303317
5751 Utot 322321
5752 Utot 304269
5753 Utot 303534
5754 Utot 410114
5755 Utot 311889
5756 Utot 292204
5757 Utot 308353
5758 Utot 343664
5759 Utot 303279
5760 Utot 336292
5761 Utot 335898
5762 Utot 345334
5763 Utot 373770
5764 Utot 352592
5765 Utot 331823
5766 Utot 390399
5767 Utot 308596
5768 Utot 307566
5769 Utot 305832
5770 Utot 305867
5771 Utot 311082
5772 Utot 335550
5773 Utot 326345
5774 Utot 285674
5775 Utot 382721
5776 Utot 345124
5777 Utot 328383
5778 Utot 300546
5779 Utot 409523
5780 Utot 302063
5781 Utot 431122
5782 Utot 314403
5783 Utot 300967
5784 Utot 323506
5785 Utot 308744
5786 Utot 327686
5787 Utot 280620
5788 Utot 359710
5789 Utot 329076
5790 Utot 293744
5791 Utot 302985
5792 Utot 318695
5793 Utot 317565
5794 Utot 316511
5795 Utot 282539
5796 Utot 394837
5797 Utot 307131
5798 Utot 299500
5799 Utot 324353
5800 Utot 368767
5801 Utot 376573
5802 Utot 364113
5803 Utot 340911
5804 Utot 363575
5805 Utot 268730
5806 Utot 295267
5807 Utot 268541
5808 Utot 332249
5809 Utot 328909
5810 Utot 315481
5811 Utot 355115
5812 Utot 376036
5813 Utot 315377
5814 Utot 382193
5815 Utot 443525
5816 Utot 318458
5817 Utot 364550
5818 Utot 329197
5819 Utot 285444
5820 Utot 367158
5821 Utot 289410
5822 Utot 388342
5823 Utot 375158
5824 Utot 298349
5825 Utot 376068
5826 Utot 437655
5827 Utot 357115
5828 Utot 333637
5829 Utot 322798
5830 Utot 340983
5831 Utot 349102
5832 Utot 383919
5833 Utot 301589
5834 Utot 304815
5835 Utot 275026
5836 Utot 328879
5837 Utot 465362
5838 Utot 340895
5839 Utot 317468
5840 Utot 292089
5841 Utot 305749
5842 Utot 333009
5843 Utot 390621
5844 Utot 459846
5845 Utot 314731
5846 Utot 317719
5847 Utot 365271
5848 Utot 309163
5849 Utot 333664
5850 Utot 307682
5851 Utot 427629
5852 Utot 323842
5853 Utot 312113
5854 Utot 295856
5855 Utot 418041
5856 Utot 309988
5857 Utot 348028
5858 Utot 297170
5859 Utot 328528
5860 Utot 306056
5861 Utot 302850
5862 Utot 303499
5863 Utot 306820
5864 Utot 330799
5865 Utot 367888
5866 Utot 291057
5867 Utot 314433
5868 Utot 273569
5869 Utot 333435
5870 Utot 336072
5871 Utot 340524
5872 Utot 298275
5873 Utot 326283
5874 Utot 317374
5875 Utot 337605
5876 Utot 282211
5877 Utot 307525
5878 Utot 313582
5879 Utot 330326
5880 Utot 299869
5881 Utot 351041
5882 Utot 320654
5883 Utot 313733
5884 Utot 323260
5885 Utot 319789
5886 Utot 317605
5887 Utot 277004
5888 Utot 293196
5889 Utot 298742
5890 Utot 330417
5891 Utot 338624
5892 Utot 351857
5893 Utot 335272
5894 Utot 328866
5895 Utot 304399
5896 Utot 369576
5897 Utot 318339
5898 Utot 333870
5899 Utot 356094
5900 Utot 287502
5901 Utot 306644
5902 Utot 340191
5903 Utot 392545
5904 Utot 317582
5905 Utot 340362
5906 Utot 313839
5907 Utot 287995
5908 Utot 290842
5909 Utot 352347
5910 Utot 324892
5911 Utot 321952
5912 Utot 370798
5913 Utot 418239
5914 Utot 279620
5915 Utot 313386
5916 Utot 302726
5917 Utot 340936
5918 Utot 290498
5919 Utot 337936
5920 Utot 311649
5921 Utot 327147
5922 Utot 371459
5923 Utot 311074
5924 Utot 353987
5925 Utot 310467
5926 Utot 303125
5927 Utot 361482
5928 Utot 342338
5929 Utot 380958
5930 Utot 334331
5931 Utot 347187
5932 Utot 363795
5933 Utot 382358
5934 Utot 370114
5935 Utot 405898
5936 Utot 335071
5937 Utot 305368
5938 Utot 381641
5939 Utot 368073
5940 Utot 329221
5941 Utot 384058
5942 Utot 354007
5943 Utot 351071
5944 Utot 279612
5945 Utot 357404
5946 Utot 333483
5947 Utot 286184
5948 Utot 311949
5949 Utot 338925
5950 Utot 374913
5951 Utot 286986
5952 Utot 301125
5953 Utot 272777
5954 Utot 287029
5955 Utot 311957
5956 Utot 326167
5957 Utot 393769
5958 Utot 292647
5959 Utot 288764
5960 Utot 278364
5961 Utot 343114
5962 Utot 367215
5963 Utot 322460
5964 Utot 359100
5965 Utot 300244
5966 Utot 308639
5967 Utot 316021
5968 Utot 322930
5969 Utot 365859
5970 Utot 355949
5971 Utot 347891
5972 Utot 334436
5973 Utot 320466
5974 Utot 331366
5975 Utot 358244
5976 Utot 351241
5977 Utot 323218
5978 Utot 333369
5979 Utot 345104
5980 Utot 382414
5981 Utot 321515
5982 Utot 334850
5983 Utot 378632
5984 Utot 342280
5985 Utot 321821
5986 Utot 339536
5987 Utot 325681
5988 Utot 331752
5989 Utot 342715
5990 Utot 323728
5991 Utot 361065
5992 Utot 326272
5993 Utot 313135
5994 Utot 274660
5995 Utot 309121
5996 Utot 329357
5997 Utot 314224
5998 Utot 345026
5999 Utot 380569
6000 Utot 334859
6001 Ntot 328407
6002 Ntot 331349
6003 Ntot 323358
6004 Ntot 310392
6005 Ntot 314010
6006 Ntot 310994
6007 Ntot 296059
6008 Ntot 293636
6009 Ntot 333368
6010 Ntot 360941
6011 Ntot 327260
6012 Ntot 295683
6013 Ntot 347724
6014 Ntot 347634
6015 Ntot 350867
6016 Ntot 358723
6017 Ntot 299358
6018 Ntot 334380
6019 Ntot 288729
6020 Ntot 346978
6021 Ntot 321194
6022 Ntot 286858
6023 Ntot 310209
6024 Ntot 292205
6025 Ntot 317943
6026 Ntot 333732
6027 Ntot 300986
6028 Ntot 321679
6029 Ntot 389103
6030 Ntot 344707
6031 Ntot 343839
6032 Ntot 324761
6033 Ntot 313557
6034 Ntot 333251
6035 Ntot 454165
6036 Ntot 350722
6037 Ntot 345390
6038 Ntot 336194
6039 Ntot 345264
6040 Ntot 362847
6041 Ntot 338913
6042 Ntot 341795
6043 Ntot 355602
6044 Ntot 299073
6045 Ntot 309670
6046 Ntot 409348
6047 Ntot 329796
6048 Ntot 345012
6049 Ntot 284567
6050 Ntot 284738
6051 Ntot 307265
6052 Ntot 416134
6053 Ntot 327967
6054 Ntot 331928
6055 Ntot 342112
6056 Ntot 366764
6057 Ntot 295186
6058 Ntot 314472
6059 Ntot 346440
6060 Ntot 284046
6061 Ntot 392750
6062 Ntot 298481
6063 Ntot 388883
6064 Ntot 334349
6065 Ntot 347644
6066 Ntot 330861
6067 Ntot 330805
6068 Ntot 332525
6069 Ntot 318246
6070 Ntot 347573
6071 Ntot 349106
6072 Ntot 329310
6073 Ntot 354218
6074 Ntot 317271
6075 Ntot 303183
6076 Ntot 342882
6077 Ntot 338125
6078 Ntot 311263
6079 Ntot 322521
6080 Ntot 291836
6081 Ntot 342376
6082 Ntot 315850
6083 Ntot 314319
6084 Ntot 306812
6085 Ntot 374313
6086 Ntot 371520
6087 Ntot 341323
6088 Ntot 327370
6089 Ntot 369748
6090 Ntot 311276
6091 Ntot 336246
6092 Ntot 277312
6093 Ntot 322052
6094 Ntot 327564
6095 Ntot 303667
6096 Ntot 319568
6097 Ntot 321821
6098 Ntot 314921
6099 Ntot 355931
6100 Ntot 286662
6101 Ntot 312405
6102 Ntot 349533
6103 Ntot 358786
6104 Ntot 332609
6105 Ntot 422554
6106 Ntot 305379
6107 Ntot 379052
6108 Ntot 292645
6109 Ntot 344993
6110 Ntot 331332
6111 Ntot 338596
6112 Ntot 325399
6113 Ntot 326290
6114 Ntot 343648
6115 Ntot 372203
6116 Ntot 331974
6117 Ntot 346818
6118 Ntot 301944
6119 Ntot 324036
6120 Ntot 348702
6121 Ntot 280667
6122 Ntot 286230
6123 Ntot 316685
6124 Ntot 406314
6125 Ntot 317744
6126 Ntot 330017
6127 Ntot 319967
6128 Ntot 344673
6129 Ntot 275993
6130 Ntot 348740
6131 Ntot 298563
6132 Ntot 317190
6133 Ntot 302557
6134 Ntot 327355
6135 Ntot 318677
6136 Ntot 386001
6137 Ntot 312264
6138 Ntot 305981
6139 Ntot 333545
6140 Ntot 353243
6141 Ntot 356042
6142 Ntot 350870
6143 Ntot 321791
6144 Ntot 336062
6145 Ntot 382098
6146 Ntot 353267
6147 Ntot 323736
6148 Ntot 372293
6149 Ntot 344669
6150 Ntot 366095
6151 Ntot 321987
6152 Ntot 332459
6153 Ntot 343811
6154 Ntot 361186
6155 Ntot 306889
6156 Ntot 320846
6157 Ntot 359877
6158 Ntot 295436
6159 Ntot 351287
6160 Ntot 342362
6161 Ntot 336683
6162 Ntot 310006
6163 Ntot 406873
6164 Ntot 300604
6165 Ntot 328737
6166 Ntot 362637
6167 Ntot 303473
6168 Ntot 312058
6169 Ntot 334709
6170 Ntot 360506
6171 Ntot 325032
6172 Ntot 318985
6173 Ntot 309286
6174 Ntot 380886
6175 Ntot 317455
6176 Ntot 308762
6177 Ntot 355788
6178 Ntot 340096
6179 Ntot 340905
6180 Ntot 399412
6181 Ntot 348754
6182 Ntot 317875
6183 Ntot 366952
6184 Ntot 360047
6185 Ntot 369207
6186 Ntot 314071
6187 Ntot 328038
6188 Ntot 308840
6189 Ntot 371757
6190 Ntot 304728
6191 Ntot 330035
6192 Ntot 329293
6193 Ntot 339386
6194 Ntot 331336
6195 Ntot 340079
6196 Ntot 386060
6197 Ntot 295014
6198 Ntot 405543
6199 Ntot 349920
6200 Ntot 350780
6201 Ntot 314514
6202 Ntot 346668
6203 Ntot 308764
6204 Ntot 323189
6205 Ntot 297452
6206 Ntot 283004
6207 Ntot 341645
6208 Ntot 315907
6209 Ntot 358967
6210 Ntot 314361
6211 Ntot 357940
6212 Ntot 281944
6213 Ntot 355882
6214 Ntot 332494
6215 Ntot 405268
6216 Ntot 328020
6217 Ntot 313649
6218 Ntot 328651
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11020 Ntot 314400
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11038 Ntot 352126
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11074 Ntot 365430
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11112 Ntot 351283
11113 Ntot 334809
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11118 Ntot 327562
11119 Ntot 332563
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11200 Ntot 370720
11201 Ntot 322526
11202 Ntot 367189
11203 Ntot 329367
11204 Ntot 319779
11205 Ntot 369371
11206 Ntot 342805
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11210 Ntot 319124
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11212 Ntot 285247
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11222 Ntot 320308
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11960 Ntot 283873
11961 Ntot 348623
11962 Ntot 372724
11963 Ntot 327969
11964 Ntot 364609
11965 Ntot 305753
11966 Ntot 314148
11967 Ntot 321530
11968 Ntot 328439
11969 Ntot 371368
11970 Ntot 361458
11971 Ntot 353400
11972 Ntot 339945
11973 Ntot 325975
11974 Ntot 336875
11975 Ntot 363753
11976 Ntot 356750
11977 Ntot 328727
11978 Ntot 338878
11979 Ntot 350613
11980 Ntot 387923
11981 Ntot 327024
11982 Ntot 340359
11983 Ntot 384141
11984 Ntot 347789
11985 Ntot 327330
11986 Ntot 345045
11987 Ntot 331190
11988 Ntot 337261
11989 Ntot 348224
11990 Ntot 329237
11991 Ntot 366574
11992 Ntot 331781
11993 Ntot 318644
11994 Ntot 280169
11995 Ntot 314630
11996 Ntot 334866
11997 Ntot 319733
11998 Ntot 350535
11999 Ntot 386078
12000 Ntot 340368
$layers
$layers[[1]]
mapping: xintercept = ~quants
geom_vline: na.rm = FALSE
stat_identity: na.rm = FALSE
position_identity
$layers[[2]]
geom_density: na.rm = FALSE, orientation = NA, outline.type = upper
stat_density: na.rm = FALSE, orientation = NA
position_identity
$layers[[3]]
mapping: label = ~paste("Posterior mean: ", post.mean, "\nPosterior sd : ", post.sd, sep = ""), vjust = 1, hjust = 1, x = Inf, y = Inf
geom_text: parse = FALSE, check_overlap = FALSE, size.unit = mm, na.rm = FALSE
stat_identity: na.rm = FALSE
position_identity
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add: function
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env: 0x7fc5d3ddc570
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attr(,"class")
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$labels
$labels$x
[1] "Value of parameter"
$labels$title
[1] "Posterior plots with 95% credible intervals"
$labels$y
[1] "density"
$labels$xintercept
[1] "quants"
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A plot of the \(logit(P)\) (the logit of the estimated probability of capture) is shown in ?@fig-btspas-diag1-logitP-nondiag
NULL
A summary of the posterior for each parameter is also available. The estimates of total abundance can be extracted and summarized in a similar fashion as in the other models:
BTSPAS.nondiag.est1 <- Petersen::LP_BTSPAS_est (BTSPAS.nondiag.fit1)
BTSPAS.nondiag.est1$summary N_hat_f N_hat_rn N_hat N_hat_SE N_hat_conf_level N_hat_conf_method
1 NA NA 337613.2 33764.97 0.95 Posterior
N_hat_LCL N_hat_UCL p_model name_model cond.ll n.parms nobs
1 285518.2 415926.8 ~1 p: ~1 NA NA 150429
The estimated total abundance from BTSPAS is 337,613 (SD 33,765 ) fish.
9 Incomplete or partial stratification
9.1 Introduction
Capture heterogeneity is known to cause bias in estimates of abundance in capture–recapture studies. This heterogeneity is often related to observable fixed characteristics of the animals such as sex. If this information can be observed for every handled animal at both sample occasions, then it is straight- forward to stratify (e.g., by sex) and obtain stratum-specific estimates.
However, it may be difficult to measure the covariate for every fish. For example, it may be difficult to sex all captured fish because morphological differences are slight or because of logistic constraints. In these cases, a subsample of the captured fish at each sample occasion is selected, and additional and often more costly measurements are made, such as sex determination through sacrificing the fish.
The resulting data now consist of two types of marked animals: animals whose value of the stratification variable is unknown, and subsamples at each occasion where the value of the stratification variables are determined.
Premarathna, Schwarz, and Jones (2018) developed methodology for these types of studies. Furthermore, given the relative costs of sampling for a simple capture and for processing the subsample, optimal allocation of effort for a given cost can be determined. They also developed methods to account for additional information (e.g., prior information about the sex ratio) and for supplemental continuous covariates such as length.
These methods were applied to a problem of estimating the size of the walleye population in Mille Lacs Lake, MN and the data are reanalyzed here.
Note that this Petersen package functions for this methods are simple wrappers around the published code from the paper. Furthermore, wrapper are available only for model without continuous covariates in the Petersen package. Contact the above authors for code for more complex cases.
The complete statistical theory is presented in Premarathna, Schwarz, and Jones (2018).
9.2 Sampling protocol
At the first sample occasion, a random sample of size \(n_1\) is captured. Then, a subsample of size \(n^∗_1\) is selected from \(n_1\), and the stratum is determined for all animals in the subsample. All captured animals are tagged, usually with a unique tag number, and released back to the population.
Again, some time later, another sample of animals of size \(n_2\) is captured randomly from the population. The animals captured at the second sample occasion contain animals captured and marked at the first occasion (some of them might be stratified and some might not be stratified), as well as animals not captured at the first occasion. One of the requirements here is that some of the stratified subsamples at the first occasion are recaptured. Also, animals must not be sacrificed to determine stratification membership at the first sample occasion. Again, a subsample of size \(n^∗_2\) is selected from the captured sample at the second sample occasion including only animals not marked at the first occasion. A pictorial view of the sampling protocol is given in Figure 24
Note that only unmarked fish are examined in the subsample at both sampling occasions
9.3 Capture histories and parameters
The parameters for this type of study are
- \(N\) - population abundance
- \(p_1\), \(p_2\) - capture probabilities at the two sampling occasions
- \(\lambda_1\),…\(\lambda_k\) the proportion of the population in the \(k\) categories. Must add to 1.
- \(\theta_1\), \(\theta_2\) - the subsampling proportions at the two occasions.
There are \(3k+4\) possible capture histories. Each history is a two-digit string with entries of 0 (not captured), U (stratification unknown), or a code for the stratification variable (e.g. M, F, etc.).
The possible histories and corresponding probabilities are:
| History | Probability |
|---|---|
| MM | \(\lambda_{M}\ p_{1M} \ \theta_1 \ p_{2M}\) |
| M0 | \(\lambda_{M} \ p_{1M} \ \theta_1 \ (1-p_{2M})\) |
| 0M | \(\lambda_{M} \ (1-p_{1M})\ p_{2M}\ \theta_{2}\) |
| \(\ldots\) | Similarly for other categories |
| UU | \(\lambda_{M} \ p_{1M}\ (1-\theta_1)\ p_{2M} + \lambda_{F} \ p_{1F} \ (1-\theta_1) \ p_{2F}\) |
| U0 | \(\lambda_{M} \ p_{1M}\ (1-\theta_1)\ (1-p_{2M}) + \lambda_{F} \ p_{1F} \ (1-\theta_1) \ (1-p_{2F})\) |
| 0U | \(\lambda_{M} \ (1-p_{1M}) \ p_{2M} \ (1-\theta_2) + \lambda_{F} \ (1-p_{1F}) \ p_{2F} \ (1-\theta_2)\) |
| 00 | Everything else (not observable) |
Note that histories such as UF are not allowed as only unmarked fish in the second sample are sub-sampled. Also histories such as MF would indicates an error.
Standard numerical likelihood methods are applied in the usual way to estimate the parameters and obtain measures of uncertainty. After estimates are obtained, stratum specific abundance estimates are obtained as \(\widehat{N}_k = \widehat{N} \times \widehat{\lambda}_k\) and measures of uncertainty obtained using the delta method.
9.4 Example - Walleye in Milles Lac, MN.
This is the data analyzed in Premarathna, Schwarz, and Jones (2018). There are some slight differences from the data in the published paper because fish that did not have length also measured are removed.
Walleye are captured on the spawning grounds. Almost all the fish can be sexed in the first occasion All the captured fish are tagged and released and the recapture occurred 3 weeks later using gill-nets From a sample of fish captured at second occasion that are not tagged, a random sample is selected and sexed.
Here is the summary data:
data(data_wae_is_short) # does not include length covariate
data_wae_is_short cap_hist freq
1 0F 237
2 0M 41
3 0U 3058
4 F0 1555
5 FF 32
6 M0 5071
7 MM 40
8 U0 42
9 UU 1
We start by fitting a model that allows for different probabilities of capture by sampling occasion and sex. Notice that we specify the “hidden” stratification variable using ..cat in the model for \(p\). It is possible to specify models for \(\lambda\) (category proportions) and \(\theta\) (subsampling fractions) but these are seldom useful (but see an example in the published paper).
Premarathna, Schwarz, and Jones (2018) provided a function to print the full results in a nice format
LP_IS_print(wae.res1)
Model information:
Model Name: p: ~-1 + ..cat:..time; theta: ~-1 + ..time; lambda: ~-1 + ..cat; offsets 0,0,0,0,0,0,0
Neg Log-Likelihood: -71018.68
Number of Parameters: 8
AICc value: -142021.4
Raw data:
$History
[1] "0F" "0M" "0U" "F0" "FF" "M0" "MM" "U0" "UU"
$counts
[1] 237 41 3058 1555 32 5071 40 42 1
$category
[1] "F" "M"
Initial values used for optimization routine:
Initial capture probabilities:
time1 time2
F 0.0214139 0.01082925
M 0.0214139 0.01082925
Initial category proportions:
lambda_ F lambda_ M
0.5 0.5
Initial sub-sample proportions:
theta_1 theta_2
0.99362112 0.08333333
Initial population size for optimization(simple Lincoln Petersen estimator is used) : 314,795
Design matrix and OFFSET vector for capture probabilities:
Beta...catF...time1 Beta...catM...time1 Beta...catF...time2
p1F 1 0 0
p1M 0 1 0
p2F 0 0 1
p2M 0 0 0
Beta...catM...time2 OFFSET.vector
p1F 0 0
p1M 0 0
p2F 0 0
p2M 1 0
Design matrix and OFFSET vector for sub-sample proportions (theta):
Beta...time1 Beta...time2 OFFSET.vector
theta_1 1 0 0
theta_2 0 1 0
Design matrix and OFFSET vector for category proportions (lambda):
..catF OFFSET.vector
lambda_F 1 0
Find MLEs:
MLEs for capture probabilities:
time1 time2
F 0.01146535 0.020643986
M 0.07658161 0.007930921
MLEs for category proportions:
lambda_ F lambda_ M
0.674743 0.325257
MLEs for sub-sample proportions:
theta_1 theta_2
0.9936211 0.0833333
MLE for Population size : 206,507
MLE for Population size of category F : 139,339
MLE for Population size of category M : 67,168
SE's of the MLEs
SE's of the MLEs of capture probabilities:
time1 time2
F 0.002009477 0.003569036
M 0.015121929 0.001240106
SE's of the MLEs of the category proportions:
lambda_ F lambda_ M
0.06017088 0.06017088
SE's of the MLEs of the sub-sample proportions:
theta_1 theta_2
0.000969662 0.004785221
SE of the MLE of the population size: 26,475
SE for Population size of category F : 24,172
SE for Population size of category M : 13,234
Observed and Expected counts for capture histories for the model p: ~-1 + ..cat:..time; theta: ~-1 + ..time; lambda: ~-1 + ..cat; offsets 0,0,0,0,0,0,0
History Observed.Counts Expected.counts Residual Standardized.Residuals
1 U0 42 42.5318920 -0.531891968 -0.081566309
2 UU 1 0.4706046 0.529395437 0.771707324
3 F0 1555 1554.6107699 0.389230058 0.009909151
4 M0 5071 5070.4718173 0.528182724 0.007510317
5 FF 32 32.7698643 -0.769864335 -0.134496611
6 MM 40 40.5349888 -0.534988778 -0.084037335
7 0F 237 236.9610300 0.038969959 0.002533033
8 0M 41 40.9922556 0.007744408 0.001209708
9 0U 3058 3057.4874952 0.512504751 0.009338016
Standardized residual plot for the model p: ~-1 + ..cat:..time; theta: ~-1 + ..time; lambda: ~-1 + ..cat; offsets 0,0,0,0,0,0,0
Estimates of abundance are found in the usual fashion, both for the entire population:
wae.est1 <- LP_IS_est(wae.res1, N_hat=~1, conf_level=0.95)
wae.est1$summary N_hat_f N_hat_conf_level N_hat_conf_method N_hat_rn N_hat N_hat_SE
1 ~1 0.95 logN All 206506.9 26474.59
N_hat_LCL N_hat_UCL p_model theta_model lambda_mode
1 160623.4 265497.4 ~-1 + ..cat:..time ~-1 + ..time ~-1 + ..cat
name_model
1 p: ~-1 + ..cat:..time; theta: ~-1 + ..time; lambda: ~-1 + ..cat; offsets 0,0,0,0,0,0,0
cond.ll n.parms nobs method
1 71018.68 8 10077 full ll
and for the individual strata:
wae.est1a <- LP_IS_est(wae.res1, N_hat=~-1+..cat, conf_level=0.95)
wae.est1a$summary N_hat_f N_hat_conf_level N_hat_conf_method N_hat_rn N_hat N_hat_SE
1 ~-1 + ..cat 0.95 logN F 139339.1 24172.49
1.1 ~-1 + ..cat 0.95 logN M 67167.8 13233.86
N_hat_LCL N_hat_UCL p_model theta_model lambda_mode
1 99176.04 195766.78 ~-1 + ..cat:..time ~-1 + ..time ~-1 + ..cat
1.1 45651.13 98825.89 ~-1 + ..cat:..time ~-1 + ..time ~-1 + ..cat
name_model
1 p: ~-1 + ..cat:..time; theta: ~-1 + ..time; lambda: ~-1 + ..cat; offsets 0,0,0,0,0,0,0
1.1 p: ~-1 + ..cat:..time; theta: ~-1 + ..time; lambda: ~-1 + ..cat; offsets 0,0,0,0,0,0,0
cond.ll n.parms nobs method
1 71018.68 8 10077 full ll
1.1 71018.68 8 10077 full ll
As with the other functions in this package, we can fit other models such as a pooled-Petersen model:
and compare models using AICc (Table 25)
aic.table <- LP_AICc(wae.res1, wae.res2)Model specification | Conditional log-likelihood | # parms | # obs | AICc | Delta | AICcWt |
|---|---|---|---|---|---|---|
p: ~-1 + ..cat:..time; theta: ~-1 + ..time; lambda: ~-1 + ..cat; offsets 0,0,0,0,0,0,0 | 71,018.68 | 8 | 10,077 | -142,021.35 | 0.00 | 1.00 |
p: ~-1 + ..time; theta: ~-1 + ..time; lambda: ~-1 + ..cat; offsets 0,0,0,0,0,0,0 | 70,786.44 | 6 | 10,077 | -141,560.86 | 460.49 | 0.00 |
and it is clear that the pooled-Petersen has no support.
Model-averaging is unnecessary given the negligible support for the second fitted model, but again can be done in the usual fashion for the entire population abundance (Table 26):
ma.table <- LP_modavg(wae.res1, wae.res2)Modnames | AICcWt | Estimate | SE |
|---|---|---|---|
p: ~-1 + ..cat:..time; theta: ~-1 + ..time; lambda: ~-1 + ..cat; offsets 0,0,0,0,0,0,0 | 1.00 | 206,507 | 26,475 |
p: ~-1 + ..time; theta: ~-1 + ..time; lambda: ~-1 + ..cat; offsets 0,0,0,0,0,0,0 | 0.00 | 314,672 | 36,232 |
Model averaged | 206,507 | 26,475 |
and for the individual categories (Table 27).
ma.table <- LP_modavg(wae.res1, wae.res2, N_hat=~-1+..cat)Modnames | AICcWt | Estimate | SE |
|---|---|---|---|
p: ~-1 + ..cat:..time; theta: ~-1 + ..time; lambda: ~-1 + ..cat; offsets 0,0,0,0,0,0,0 | 1.00 | 139,339 | 24,172 |
p: ~-1 + ..time; theta: ~-1 + ..time; lambda: ~-1 + ..cat; offsets 0,0,0,0,0,0,0 | 0.00 | 82,275 | 9,617 |
Model averaged | 139,339 | 24,172 | |
p: ~-1 + ..cat:..time; theta: ~-1 + ..time; lambda: ~-1 + ..cat; offsets 0,0,0,0,0,0,0 | 1.00 | 67,168 | 13,234 |
p: ~-1 + ..time; theta: ~-1 + ..time; lambda: ~-1 + ..cat; offsets 0,0,0,0,0,0,0 | 0.00 | 232,398 | 26,810 |
Model averaged | 67,168 | 13,234 |
9.5 Optimal allocation
In an incomplete-stratified two-sample capture–recapture study, there is a cost to capturing an animal at each sample occasion, a cost to identify the category of the captured animal in the subsamples, and also a fixed cost regardless of the sample size. If there is a fixed amount of funds (\(C_0\)) to be used in the study, then the objective is to find the optimal number of animals to capture at both sample occasions and the optimal sizes of the subsamples to be categorized so that the variance of the estimated population abundance (\(Var(\widehat{N})\)) is minimized.
The total cost (\(C\)) of the study can be considered as a linear function of sample sizes and is given by \[C = c_f+ n_1 c_1 + n^∗_1 c^∗_1 + n_2c_2 +n^∗_2c^∗_2 ≤ C_0\] where
- \(n^*_1 \le n_1\)
- \(n^*_2 \le n_2 - E(n_{UU}+\sum_C{n_{cc}})\)
Numerical optimization methods can be used to find the optimal allocation of \(n_1\), \(n_2\), \(n^∗_1\), and \(n^*_2\) with respect to the linear constraint such that Var(\(\widehat{N}\)) is minimized.
The following costs were considered for the analysis of optimal allocation:
- \(c_f = 0\),
- \(c_1 = 4\),
- \(c^∗_1 = 0.4\),
- \(c_2 = 6\),
- \(c^∗_2 = 0.4\), and
- \(C_0 = 90,000\).
These costs are the time in minutes for the operation on a fish. A value of \(C_0 = 90,000\) minutes (i.e., 1,500 h) available for this study.
Optimal allocation suitable guesstimates for the parameters using previous studies or the researcher’s experience. We used the following guesstimates for the parameters:
- \(N=209,000\),
- \(\lambda_M =0.33\),
- \(r_1 =6.5\), and
- \(r_2 =0.4\)
where \(r_1\) is the guesstimate of the ratio of \(p_{1M}∕p_{1F}\), and \(r_2\) is the guesstimate of the ratio of \(p_{2M}∕p_{2F}\).
It is difficult to give guesstimates for capture probabilities for each category at each sample occasion. However, in practice, we can give a ratio of the capture probabilities at each sample occasion. For example, if detection probability of males is half that of females at the first sample occasion, then the ratio \(r_1\) is 0.5. The guesstimates of the ratios \(r_1\) and \(r_2\) given above are calculated using the estimates for capture probabilities see previously.
Optimal allocations of sample sizes and subsample sizes produced by numerical methods for the given costs are \(n_1 = 8,929\), \(n^∗_1 =8,908\), \(n_2 =8,359\), and \(n^∗_2= 1,412\). At the optimal allocation, \(SE(\widehat{N})=13,657\) which is 50% lower than the SE obtained using the current allocation.
Different solutions are available for \(n_1\), \(n_2\), \(n^∗_1\), and \(n^∗_2\) at optimal allocation. Conditional contour plots were used to see these different solutions. A conditional contour plot in this situation is a contour plot for the standard error of \(\widehat{N}\) where two values of \(n_1\), \(n_2\), \(n^∗_1\), or \(n^∗_2\) are fixed at the optimal values. A conditional contour plot for standard error of \(\widehat{N}\)̂ when \(n^∗_1\) and \(n^∗_2\) are fixed at the optimal values and when \(n_1\) and \(n_2\) are fixed at the optimal values are given in Figure 25. These contour plots show that many solutions are possible for optimal allocation.
Full \(R\) code is available from the paper authors.
9.6 Additional details
Premarathna, Schwarz, and Jones (2018) also provide details on
- determining the sample size for detecting differential catchabilities (power analysis);
- determining the approximate standard error to be expected under proposed sample sizes (sample size analysis),
- performing goodness-of-fit test for the chosen model,
- using individual covariates (such a length) and an conditional likelihood approach, and
- using a Bayesian analysis to incorporate outside information (such as the sex ratio).
Please consult their paper for more details.
We need to consider the issue of nonidentifiability in model fitting. All the parameters can be estimated in two-sample capture–recapture studies similar to Lincoln–Peterson (Williams et al., 2002) model fitting. However, we would not be able to estimate some of the parameters, for example, if no females were observed. There is no nonidentifiable issue on model fitting with walleye data because both males and females were observed. However, there can be a nonidentifiability issue with the population abundance parameter when modeling with individual heterogeneity, as described by Link (2003).
10 Double tagging studies to account for tag loss or non-reporting
10.1 Introduction
Tag loss is one of the few violations of assumptions that can be most easily accounted for by a modification of the sampling protocol.
Tag loss leads to a positive bias in estimates of population size because fewer tagged fish are “apparently” recovered, i.e., fish that lost tags look as if they are untagged. In order to estimate and to adjust for tag loss, some (or all) of the fish released must be double tagged.
The analysis of double tagging studies was described by Gulland (1963), Beverton and Holt (1957), Seber and Felton (1981) and Hyun et al (2012). Seber (1982) and Weatherall (1982) have a nice summary of dealing with tag loss and ad hoc adjustments to estimates of abundance. It is generally assumed that a fish that loses it tags is indistinguishable from fish that were not tagged originally.
This double tagging generally takes two forms:
- two identical or two different tags are applied. Either or both could be lost, and the retention probability could be different for each tag.
- a permanent mark (such a fin clip or a permanent dye injection or a ‘genetic tag’) is a applied. Fish that are recovered with the permanent mark but without a tag are known to have lost a tag, but the individual cannot be determined.
When double tagging fish, tag 1 of the double tag should be the same type and placed in the same location on the fish as singly tagged fish. If tags have tag numbers inscribed on the fish, you can identify from a recovery of a fish with a single tag, if it was singly or doubly tagged. Hyun et al (2012) used a different colored tags for the double tagged fish so that a fish with a single tag captured at the second event can be classified as either initially singly or doubly tagged.
The second tag can be the same tag type placed in a different location, a different tag (e.g. a PIT tag), or a permanent batch mark.
Models with a permanent double-tag are simplification of the models with tags than can be lost where the tag retention probability is set to 1. Some care is needed if a batch mark is used because you may also need to know the stratum of release. If the stratum of release is based of fish characteristics, then these can usually be measured at the second event, but if the stratum of release is based on geographic or temporal strata, then the batch mark may not be sufficient to identify the stratum of release.
Tag loss has been traditionally divided into two types (Beverton and Holt, 1957):
- Type I losses are losses that occur immediately after tagging, e.g. immediate tag shedding. This type of tag loss reduces the effective number of tags initially put out.
- Type II losses are those that happen steadily and gradually over an extended period of time following release of the tagged fish.
In a simple Petersen study, the two types of tag loss cannot be distinguished and the total tag loss between the two sampling occasions is estimated. If the exact time at liberty of tags is known, then Weatherall (1982) reviews how to estimate the two types of losses. If multiple sampling occasions take place (i.e., a Jolly-Seber study), Arnason and Mills (1981), and McDonald, Amstrup and Manly (2003) examine the biases that can be introduced, and Cowen and Schwarz (2006) develops methodology to correct for tag loss.
The Petersen package can deal with three types of double tagging studies:
- Two indistinguishable double tags are used so that if a fish is recovered with only one of the double tags, you do not know which tag was lost. This type of studies often occurs when fish are not directly handled so tag numbers inscribed on the tag cannot be read. Similarly, the tags must placed close together so that it is difficult to distinguish. If for example, double tags were placed on the left and right of a fish, or front and back of a fish, then this may an example of the second case.
- Two distinguishable double tags are used so that if a fish is recovered with only one of the double tags, you do know which of the double tags were lost. For example, every tag could have a unique tag number; or applied to the left/right side of a fish
- A permanent batch mark (e.g., fin clip) is applied that is assumed cannot be lost.
10.2 Capture histories
The apparent capture history of a fish is again denoted using \(\omega\). It is important to remember that the apparent capture-history may not reflect the underlying actual capture history. For example, a tagged fish could lose all its tags before being recaptured at the second event. This capture looks like the capture of an untagged fish, but actually is a double counting of a fish with a different apparent capture history.
The apparent capture history is expanded to also reflect the observed tagging status. A two-digit code is code for each sample event, with the first digit (0 or 1) indicating if tag 1 is present on the fish and the second value (0 or 1) indicating if tag 2 is present on the fish.
Each component of the tag-history vector is generalized to represent the status of each tag at each capture occasion Cowen and Schwarz (2006). For example, here are the possible history vectors when double tagging is performed:
For fish that received a single tag, possible histories are:
- (10 10): Fish single tagged with tag type \(A\) at occasion 1 and recaptured at sampling occasion 2.
- (10 00): Fish single tagged with tag type \(A\) at occasion 1 that are “not seen” at occasion 2. Note that this consists of fish which have retained their tag and were not captured at occasion 2 and fish that lost their tag and were recaptured at occasion 2. The latter are not recognizable has having being previously tagged.
For fish that received two indistinguishable double tags, possible histories are:
- (11 00): Fish double tagged but not recaptured with at least one of its tags present.
- (11 1X): One of the double tags was present, but it is not known which
- (11 11): Fish double tagged and recovered with both tags present.
For fish that received two distinguishable double tags, the history (11,1x) is divided into
- (11 10): Fish double tagged with tag types \(B\) at occasion 1, and recaptured only with the double tag in location 1
- (11 01): Similar to above, but now recaptured with double tag in location 2 only present
For fish that received a permanent second tag, possible histories are:
- (1P 00): Fish double tagged, but not recaptured with at least one of its tags present.
- (1P 0P): Fish double tagged, but one tag (non permanent) has been lose
- (1P 1P): Fish double tagged, and recovered with both tags present.
Finally, we have fish that apparently are recaptured for the first time at the second event.
- {00 10}: Fish that apparently are seen for the first time at the second sampling occasion. This includes fish captured for the first time at the second occasion, and also fish that were tagged at occasion 1, lost their tag(s) between the two sampling occasions, and were recaptured at occasion 2.
Now, in the case with two distinguishable tags \[n_1 = n_{1010} + n_{1000} + n_{1111} + n_{1101} + n_{1110} + n_{1100}\] \[n_2 = n_{1010} + n_{1101} + n_{1110} + n_{1111} + n_{0010}\]
but a complete count of recaptured fish cannot be made because some fish lost all their tags and were captured and so have an apparent history of (00 10).
Similar equations can be derived for the other two cases.
The number of each fish in the study with the observed capture history is the frequency count and is denoted as \(n_{\omega}\).
The additional parameters to be introduced into the model are the tag retention probabilities at the two locations (\(\rho_1\), and \(\rho_2\)) and the proportion of fish that are single tagged at the first sampling occasion, \(p_{ST}\) which is assumed to be known given the ratio of single and double tagging done at the first sampling occasion.
A complete likelihood analysis based on capture histories is quite complex because of fish that loose all their tags and are recaptured. Hyun et al (2012) developed a likelihood-approach based on the summary statistics, but this does not easily allow for stratification, or if the capture and/or tagloss retention probabilities depend on covariates. In Appendix C we present a conditional likelihood approach similar to the approach used in the conditional likelihood Petersen estimator.
In this conditional likelihood approach we condition on fish captured at the second event and ignore histories of fish tagged and never seen again. This is a sensible approach because we cannot estimate the capture probability at the second event because the apparent untagged animals captured at the second occasion are mixture of truly untagged fish and fish that were captured at the first sampling occasion and lost all their tags. Then a HT-type estimator is used to estimate the abundance using the number of fish captured at the first occasion. Consequently, you can only develop a model for the catchability at the first sampling event (e.g., depends on discrete or continuous covariates).
- try and double tag as many fish as possible, esp if tag retention is low
- one of the double tags should match the single tag other wise you have 3 tag types and not much can be done.
- hypothesis test for tagging of the form “no tag loss” are silly. If any tag loss is observed, then then hypothesis is obviously rejected. If tag loss is very low, then you can fit a simple Petersen study and live with the small bias.
10.4 Example - Simulated data - two tags that can be distinguished
Simulated data are used for this example. Tried but could not find numerical example in literature
The observed capture history data is:
data(data_sim_tagloss_twoD)
data_sim_tagloss_twoD[,-(1:2)] cap_hist freq
1 0010 879
2 1000 225
3 1010 14
4 1100 666
5 1101 21
6 1110 7
7 1111 37
Notice that we now have histories (11,01) and (11,10) compared to the previous example where these were “combined” into history (11,1X).
We can not fit models with and without equal tag retention probabilities and compare them in the usual fashion.
10.4.1 Model with equal tag retention probabilies
First, the model with equal retention probabilities across the two tag locations:
twoD.res1 <- LP_TL_fit(data_sim_tagloss_twoD,
dt_type="twoD",
p_model=~1,
rho_model=~1)
twoD.est1 <- LP_TL_est(twoD.res1, N_hat=~1, conf_level=0.95)
twoD.est1$summary N_hat_f N_hat_rn N_hat N_hat_SE N_hat_conf_level N_hat_conf_method
1 ~1 (Intercept) 10267.11 1214.854 0.95 logN
N_hat_LCL N_hat_UCL p_model rho_model name_model cond.ll n.parms nobs
1 8141.981 12946.92 ~1 ~1 p1: ~1; rho: ~1 -373.7071 2 1849
method
1 LP_TS CondLik
Estimates of the tag retention probability is
twoD.est1$detail$data.expand[1:2,c("..tag","rho","rho.se")] ..tag rho rho.se
1 1 0.7213776 0.04992898
1.1 2 0.7213776 0.04992898
10.4.2 Model with unequal tag retention probabilies
Second, a model with unequal retention probabilities across the two tag locations is fit
twoD.res2 <- LP_TL_fit(data_sim_tagloss_twoD,
dt_type="twoD",
p_model=~1,
rho_model=~-1+..tag)
twoD.est2 <- LP_TL_est(twoD.res2, N_hat=~1, conf_level=0.95)
twoD.est2$summary N_hat_f N_hat_rn N_hat N_hat_SE N_hat_conf_level N_hat_conf_method
1 ~1 (Intercept) 10196.2 1194.993 0.95 logN
N_hat_LCL N_hat_UCL p_model rho_model name_model cond.ll
1 8103.591 12829.18 ~1 ~-1 + ..tag p1: ~1; rho: ~-1 + ..tag -369.8691
n.parms nobs method
1 3 1849 LP_TS CondLik
Note the use of the ..tag variable in the formula for rho indicating that tag location is a factor that influences the retention probability.
Estimates of the different tag retention probabilities are
twoD.est2$detail$data.expand[1:2,c("..tag","rho","rho.se")] ..tag rho rho.se
1 1 0.6363982 0.06085315
1.1 2 0.8409085 0.05514061
10.4.3 Comparing models and model averaged estimates of abundance
We compare the two models in the usual way (Table 28) and obtain the model averaged estimates of abundance (Table 29).
sim.twoD.aictab <- LP_AICc(
twoD.res1,
twoD.res2
)Model specification | Conditional log-likelihood | # parms | # obs | AICc | Delta | AICcWt |
|---|---|---|---|---|---|---|
p: ~1; rho: ~-1 + ..tag | -369.8691 | 3 | 958 | 745.76 | 0.00 | 0.94 |
p: ~1; rho: ~1 | -373.7071 | 2 | 958 | 751.43 | 5.66 | 0.06 |
Most weight is given to the model with different tag retention probabilities.
# extract the estimates of the abundance
sim.twoD.ma.N_hat<- LP_modavg(
twoD.res1,
twoD.res2, N_hat=~1) Modnames | AICcWt | Estimate | SE |
|---|---|---|---|
p1: ~1; rho: ~-1 + ..tag | 0.94 | 10,196 | 1,195 |
p1: ~1; rho: ~1 | 0.06 | 10,267 | 1,215 |
Model averaged | 10,200 | 1,196 |
10.5 Example - Simulated data - a permanent second tag used
Simulated data are used for this example. Tried but could not find numerical example in literature
The observed capture history data is:
data(data_sim_tagloss_t2perm)
data_sim_tagloss_t2perm[,-(1:2)] cap_hist freq
1 0010 923
2 1000 254
3 1010 17
4 1P00 668
5 1P0P 26
6 1P1P 59
We can now fit models but the model for the tag retention probability cannot depend on the tag number since the permanent tag has retention probability of 1.
t2perm.res1 <- LP_TL_fit(data_sim_tagloss_t2perm,
dt_type="t2perm",
p_model=~1,
rho_model=~1)
t2perm.est1 <- LP_TL_est(t2perm.res1, N_hat=~1, conf_level=0.95)
t2perm.est1$summary N_hat_f N_hat_rn N_hat N_hat_SE N_hat_conf_level N_hat_conf_method
1 ~1 (Intercept) 9425.522 937.881 0.95 logN
N_hat_LCL N_hat_UCL p_model rho_model name_model cond.ll n.parms nobs
1 7755.452 11455.23 ~1 ~1 p1: ~1; rho: ~1 -430.7471 2 1947
method
1 LP_TS CondLik
Estimates of the probability of capture at the first event, and the tag retention probabilities are
t2perm.est1$detail$data[1, c('p1',"p1.se")] p1 p1.se
1 0.1086412 0.01032415
t2perm.est1$detail$data.expand[1:2,c("..tag","rho","rho.se")] ..tag rho rho.se
1 1 0.6824881 0.04923361
1.1 2 1.0000000 0.00000000
10.6 Example - Northern Pike - tag loss
In Section 6.2, we analyzed the Northern Pike data assuming that tag loss was negligible. In this example, we will estimate the tag retention probability and show that the conditional likelihood tagloss models can include more complex effects.
Refer to Section 6.2 for information on the sampling design.
We load the data in the usual fashion:
data(data_NorthernPike_tagloss)
data_NorthernPike_tagloss[1:5,] cap_hist Sex Length freq
1 0010 m 23.20 1
2 0010 f 28.89 1
3 0010 m 25.20 1
4 0010 m 22.20 1
5 0010 m 25.00 1
Fish with histories 1110 and 1101 are pooled into capture history 111X and only models with equal retention probabilities for the two tags can be fit.
We start with a basic model, where capture probabilities and tag-retention probabilities don’t vary over the fish. The estimate of abundance is:
nop.TL.res1 <- LP_TL_fit(data_NorthernPike_tagloss,
dt_type="notD",
p_model=~1,
rho_model=~1)
nop.TL.est1 <- LP_TL_est(nop.TL.res1, N_hat=~1, conf_level=0.95)
nop.TL.est1$summary N_hat_f N_hat_rn N_hat N_hat_SE N_hat_conf_level N_hat_conf_method
1 ~1 (Intercept) 49516.75 3711.682 0.95 logN
N_hat_LCL N_hat_UCL p_model rho_model name_model cond.ll n.parms nobs
1 42751.13 57353.06 ~1 ~1 p1: ~1; rho: ~1 -482.3847 2 7805
method
1 LP_TS CondLik
Estimates of the tag retention probability is
nop.TL.est1$detail$data.expand[1:2,c("..tag","rho","rho.se")] ..tag rho rho.se
1 1 0.9805195 0.007951377
1.1 2 0.9805195 0.007951377
So estimated tag retention was over 98%, and that is why tag loss was previously ignored.
We now fit a model stratified by sex and the estimate of overall abundance is now:
nop.TL.res2 <- LP_TL_fit(data_NorthernPike_tagloss,
dt_type="notD",
p_model=~Sex,
rho_model=~1)
nop.TL.est2 <- LP_TL_est(nop.TL.res2, N_hat=~1, conf_level=0.95)
nop.TL.est2$summary N_hat_f N_hat_rn N_hat N_hat_SE N_hat_conf_level N_hat_conf_method
1 ~1 (Intercept) 49363.51 3699.588 0.95 logN
N_hat_LCL N_hat_UCL p_model rho_model name_model cond.ll n.parms
1 42619.86 57174.19 ~Sex ~1 p1: ~Sex; rho: ~1 -482.0723 3
nobs method
1 7805 LP_TS CondLik
Finally, we allow the tag retention probabilities to also vary by sex and the estimated overall abundance is:
nop.TL.res3 <- LP_TL_fit(data_NorthernPike_tagloss,
dt_type="notD",
p_model=~Sex,
rho_model=~Sex)
nop.TL.est3 <- LP_TL_est(nop.TL.res3, N_hat=~1, conf_level=0.95)
nop.TL.est3$summary N_hat_f N_hat_rn N_hat N_hat_SE N_hat_conf_level N_hat_conf_method
1 ~1 (Intercept) 49363.12 3699.555 0.95 logN
N_hat_LCL N_hat_UCL p_model rho_model name_model cond.ll n.parms
1 42619.53 57173.73 ~Sex ~Sex p1: ~Sex; rho: ~Sex -482.016 4
nobs method
1 7805 LP_TS CondLik
Estimates of the tag retention probability for the two sexes are
firstm <- match("m", nop.TL.est3$detail$data.expand$Sex)
firstf <- match("f", nop.TL.est3$detail$data.expand$Sex)
nop.TL.est3$detail$data.expand[sort(c(firstm, firstm+1, firstf, firstf+1)),c("Sex","..tag","rho","rho.se")] Sex ..tag rho rho.se
1 m 1 0.9774436 0.013019620
1.1 m 2 0.9774436 0.013019620
2 f 1 0.9828572 0.009895976
2.1 f 2 0.9828572 0.009895976
The tag retention probabilities are very similar across the two sexes.
The usual model averaging can be done as shown in Table 30.
nop.TL.aictab <- Petersen::LP_AICc (
nop.TL.res1,
nop.TL.res2,
nop.TL.res3
)Model specification | Conditional log-likelihood | # parms | # obs | AICc | Delta | AICcWt |
|---|---|---|---|---|---|---|
p: ~1; rho: ~1 | -482.3847 | 2 | 1,134 | 968.78 | 0.00 | 0.59 |
p: ~Sex; rho: ~1 | -482.0723 | 3 | 1,134 | 970.17 | 1.39 | 0.30 |
p: ~Sex; rho: ~Sex | -482.0160 | 4 | 1,134 | 972.07 | 3.29 | 0.11 |
Most of the model weight is on the simplest model. The model averaged overall abundance estimate are (Table 31)
nop.TL.modavg <- Petersen::LP_modavg (
nop.TL.res1,
nop.TL.res2,
nop.TL.res3
)N_hat_f | N_hat_rn | Modnames | AICcWt | Estimate | SE |
|---|---|---|---|---|---|
~1 | (Intercept) | p1: ~1; rho: ~1 | 0.59 | 49,517 | 3,712 |
~1 | (Intercept) | p1: ~Sex; rho: ~1 | 0.30 | 49,364 | 3,700 |
~1 | (Intercept) | p1: ~Sex; rho: ~Sex | 0.12 | 49,363 | 3,700 |
Model averaged | 49,454 | 3,707 |
10.7 Example - Simulated data - non-reporting of tags and reward tags
One assumption of the Petersen estimator is that all recovered tags are reported. However, some studies relies on returns from anglers or other citizens, and not all tags may be reported. To estimate the reporting probability, a second type of tag (the “reward” tag) is applied that often has a monetary incentive to return. The monetary incentive should be large enough that the reporting probability for these tags is 100%.
These types of studies can also be analyzed using the tagloss models. The reward tag is treated as a permanent tag.
Simulated data are used for this example. The observed capture history data is:
data(data_sim_reward)
data_sim_reward cap_hist freq
1 0010 930
2 0P00 207
3 0P0P 23
4 1000 712
5 1010 56
In this example, about 1500 non-reward tags were applied, and about 230 reward tags were applied. No fish has both types of tags. The reporting probability is estimated by the ratio of the tags returned
# estimate return probability and empirical SE
t1.applied <- sum(data_sim_reward$freq[ data_sim_reward$cap_hist %in% c("1000","1010")])
t1.returned <- sum(data_sim_reward$freq[ data_sim_reward$cap_hist %in% c( "1010")])
t2.applied <- sum(data_sim_reward$freq[ data_sim_reward$cap_hist %in% c("0P0P","0P00")])
t2.returned <- sum(data_sim_reward$freq[ data_sim_reward$cap_hist %in% c("0P0P" )])
rr <- (t1.returned/t1.applied) / (t2.returned/t2.applied)
rr.se <- sd( rbeta(10000, t1.returned, t1.applied-t1.returned)/ rbeta(10000, t2.returned, t2.applied-t2.returned))and is estimated as 0.729 (SE 0.189).
We can now fit the permanent tag models as seen previously and obtain estimates of abundance:
reward.res1 <- LP_TL_fit(data_sim_reward,
dt_type="t2perm",
p_model=~1,
rho_model=~1)
reward.est1 <- LP_TL_est(reward.res1, N_hat=~1, conf_level=0.95)
reward.est1$summary N_hat_f N_hat_rn N_hat N_hat_SE N_hat_conf_level N_hat_conf_method
1 ~1 (Intercept) 10090.01 2101.777 0.95 logN
N_hat_LCL N_hat_UCL p_model rho_model name_model cond.ll n.parms nobs
1 6707.858 15177.46 ~1 ~1 p1: ~1; rho: ~1 -324.7077 2 1928
method
1 LP_TS CondLik
Estimates of the probability of capture at the first event, and the tag reporting probability are
reward.est1$detail$data[1, c('p1',"p1.se")] p1 p1.se
1 0.09890973 0.02038768
reward.est1$detail$data.expand[1:2,c("..tag","rho","rho.se")] ..tag rho rho.se
1 1 0.7291672 0.1805853
1.1 2 1.0000000 0.0000000
10.8 Planning tag loss studies
As a general rule, unless you have good information on tag retention probabilities, it is better to assume the worst and plan studies under the pessimistic assumption that tag loss will occur. The primary question is then how many fish should be double tagged?
This is a trade off because it is more costly to actually double tag fish, both when applying tags, but also in recording tag numbers, etc. There are additional tagging costs etc.
The easiest way to investigate the optimal sampling design is via simulation.
10.8.1 Example of deciding between proportion of double tagging
Suppose that you have $15,000 for tagging operations and that double tagging a fish costs 2x as much as single tagging a fish in supplies (more tags) and additional labor. We can simulate a tagging data set with various parameters, and then compare the precision (SE) as a function of the number of double tagged fish.
We start by making some assumptions about the
- abundance say, 10,000 fish.
- tag retention probabilities (say 0.80 for all fish)
- effort at the second sample, say 1000 fish can be examined.
We first generate the scenarios that we wish to compare
scenarios <- expand.grid(N=10000,
rho1=0.80,
rho2=0.80,
n2=1000,
n1.dt=seq(50, 500, 50),# number of double tags
n.sim=10) # simulations per scenario
scenarios$n1.st <- 1500 - scenarios$n1.dt*3 # how many single tags can be applied
scenarios$n1 <- scenarios$n1.st + scenarios$n1.dt
scenarios$pST<- scenarios$n1.st/ scenarios$n1
scenarios$index <- 1:nrow(scenarios)
scenarios N rho1 rho2 n2 n1.dt n.sim n1.st n1 pST index
1 10000 0.8 0.8 1000 50 10 1350 1400 0.9642857 1
2 10000 0.8 0.8 1000 100 10 1200 1300 0.9230769 2
3 10000 0.8 0.8 1000 150 10 1050 1200 0.8750000 3
4 10000 0.8 0.8 1000 200 10 900 1100 0.8181818 4
5 10000 0.8 0.8 1000 250 10 750 1000 0.7500000 5
6 10000 0.8 0.8 1000 300 10 600 900 0.6666667 6
7 10000 0.8 0.8 1000 350 10 450 800 0.5625000 7
8 10000 0.8 0.8 1000 400 10 300 700 0.4285714 8
9 10000 0.8 0.8 1000 450 10 150 600 0.2500000 9
10 10000 0.8 0.8 1000 500 10 0 500 0.0000000 10
As more fish are double tagged, the total number of tagged fish declines.
Now for each scenario, we simulate some data, analyze it using the notD tag loss model and plot the estimated precision vs number of double tags (Figure 26)
The wiggliness of the line is due to the small number of simulations run for each scenario.
We see that the SE of \(\widehat{N}\) declines rapidly as you increase the number of double tagged fish to about 200, and then slowly increases because the gain in precision from estimating the tag retention probabilities better with more double tagged fish is offset by the loss in precision by tagging fewer fish.
11 Multiple marks
11.1 Introduction
In some cases, multiple marks can be applied to an animal, but not all marks can be read for an encountered animal. The most common example of this are capture-recapture studies using natural marks found on the left or right side of an animals and “captures” are photographs.
Unfortunately, use of photo-identification records in mark–recapture analyses is not entirely without its problems. For instance, when natural markings are bilaterally asymmetrical, matching photographs to individuals can be difficult when investigators are routinely able to photograph only one side of an animal. The typical approach in the literature when confronted with this situation is to conduct separate analyses with left-sided and right-sided photographs and compare the results. The same animal may be “captured” more than once in a sampling event, but the two records, from the right or left side of the animal, cannot be matched.
Bonner and Holmberg (2013) and McClintock et al. (2013) simultaneously presented the theory for these analyses and McClintock (2015) created an R package (multimark) for the analysis of these experiment.
Much of the following is taken from these papers as applied to a two-sample (Petersen-type) experiment.
11.2 Theory
Consider a “typical” Petersen capture–recapture experiment where sampling is conducted over 2 sampling occasions and the identity of each animal is known with certainty when it is observed based on applied tags or marks. As seen previously, there are four possible encounter histories, three of which are directly observable:
- 01 (encountered on the second occasion but not the first),
- 10 (encountered on the first occasion but not the second), and
- 11 (encountered on both occasions),
- 00 (not encountered on either sampling event)- not observable.
In contrast to the preceding scenario, now consider the situation in which individuals are encountered via photographs and marks are bilaterally asymmetrical.
We will consider two photo-sampling scenarios, where on each sampling event, a
- 0 represents a non-encounter,
- L represents an encounter on the left side only as L,
- R represents an encounter on right-sided only, and
- B represent an encounter on both sides. Depending on the design of camera surveys, B encounters may be recorded from a single image (where both sides of an individual are visible), a pair of synchronized images, or multiple images (assuming both sides of an individual are known.
One-sided analyses are common for bilateral encounter data when researchers are unable to match opposite sides, but are able to accurately match left sides to left sides and right sides to right sides. Under these conditions, attempts to combine left- and right-sided encounters into a single analysis are problematic because detected individuals can yield a number of possible recorded histories, depending on whether B encounters are observable. For example, when presented with the recorded histories L0 and 0R, we do not know whether these observations arose from the same animal seen on both occasions, or whether it was indeed two different animals each seen on one occasion. Similarly, when B detections are not observed, the recorded histories L0 and R0 could arise from a single animal or from two different animals.
This is a similar issue as seen when analyzing double tagging experiments with tag loss.
There are two different data types that can be collected:
- only the left or right side (LR data type) or
- the left, right, or both sides (LRB data type). Depending on the design of camera surveys, B encounters may be recorded from a single image (where both sides of an individual are visible), a pair of synchronized images, or multiple images (assuming both sides of an individual are known.
Now for any one particular animal, there are 16 possible (latent) encounter histories that give rise to the observable encounter histories (Table 32).
Column 4 in Table 32 indicates which underlying (latent) encounter histories are mapped to the observable encounter histories. For example, an animal not seen in the first sampling event, and then both sides seen the second sampling event (OB, forth row), gives rise to two observable (recorded) histories (0L and 0R) in experiment where both sides can never be matched to a single animal.
The parameters of this model are
- \(N\) abundance
- \(p_t\) encounter probability at sampling event \(t\)
- \(\delta^L\) probability that an individual which is encountered has its Left side photographed
- \(\delta^R\) probability that an individual which is encountered has its right side photographed
- \(\delta^B\) probability that an individual which is encountered has both sides photographed
These parameters can be used to compute the probability of each underlying (latent) encounter history (column 3 in Table 32). These probabilities must sum to 1 over all latent encounter histories. Now many of the latent encounter histories are mapped to multiple recorded histories. Their probabilities will no longer sum to 1 because many latent histories are double counted, and the counts from the reported histories (columns 6 and 9) no longer follow a multinomial distribution.
Because of this potential double counting, a likelihood analysis is very difficult and both Bonner and Holmberg (2013) and McClintock et al (2013) developed a Bayesian approach. Their papers should be consulted for details. McClintock (2015) developed an R package (multimark) that performs the Bayesian analysis using Monte Carlo Markov Chain (MCMC) methods which will be illustrated below.
By referring to Table 32, the expected counts for each of the capture histories under the LR protocol are:
- \(E[ n_{L0}] = N p_1 (1-\delta_R) (1-p_2 + p_2 \delta_R))\)
- \(E[ n_{LL}] = N p_1 (1-\delta_R) p_2 (1-\delta_R))\)
- \(E[ n_{0L}] = N (1-p_1+p_1\delta_R) p_2 (1-\delta_R))\)
- \(E[ n_{R0}] = N p_1 (1-\delta_L) (1-p_2 + p_2 \delta_L))\)
- \(E[ n_{RR}] = N p_1 (1-\delta_L) p_2 (1-\delta_L))\)
- \(E[ n_{0R}] = N (1-p_1+p_1\delta_L) p_2 (1-\delta_L))\)
Notice that \(\delta_L + \delta_R + \delta_B=1\).
Two Petersen estimators for abundance can be found by using the animals tagged on the Left or tagged on the Right exclusively, i.e.,
\[\widehat{N}_L = \frac{(n_{L0}+n_{LL}){(n_{0L}+n_{LL})}}{n_{LL}}\] \[\widehat{N}_R = \frac{(n_{R0}+n_{RR}){(n_{0R}+n_{RR})}}{n_{RR}}\] By substituting in the expected values, we see that these estimators are consistent for \(N\).
The two estimates could be averaged in some fashion, but computing the SE of the combined estimate is complex because of the correlation in the the estimates.
Unfortunately, it is not possible to estimate \(p_1\), \(p_2\), \(\delta_L\) or \(\delta_R\) individually. But we can estimate, for example
\[\widehat{p_1(1-\delta_R)} = \frac{n_{LL}}{(n_{LL}+n_{OL})}\] which is an estimate of “Left side” catchability at time 1.
We can also estimate \[\widehat{\frac{(1-\delta_R)}{(1-\delta_L)}} = \frac{(n_{LL}+n_{L0})}{(n_{RR}+n_{R0})} \]
which is ratio of the complement of the conditional probabilities of detection on Left or Right. But the individual values of \(\delta_L\) and \(\delta_R\) cannot be found.
The latter will have implications when using multimark. If for example, left or right conditional probabilities are equal (which seems sensible for many species and experimental setups), then any value for \(\delta_L=\delta_R\) between 0 and 0.5 gives a ratio of the complements equal to 1. Hence the \(\delta\) values are non-identifiable individually, and the program will converge to a value dictated by the prior distribution for \(\delta\). Similarly, the individual estimates of \(p_1\) and \(p_2\) will depend on the final value for the \(\delta\) values and may be nonsensical. But incredibly, estimates of \(N\) will be valid!
This will be illustrated using simulated data.
However, if allow for some animals to have both sides recorded, then not only are the estimates of abundance unbiased, but you also get unbiased estimates of catchability delta.
11.3 Illustration of using multimark with simulated data.
11.3.1 LR-type surveys
The multimark package has a simulation function to generate data. We will simulate a population of 5000 individuals with different capture probabilities at the two sample times, but equal \(\delta\) values. Notice that multimark uses \(\delta_1\) for \(\delta_L\), etc. In this simulation, no animals have both sides recorded.
logit <- function (p){ log(p/(1-p))}
expit <- function(theta){ 1/(1+exp(-theta))}
set.seed(234324)
N= 5000
p1= .5
p2 = .7
test <- multimark::simdataClosed(
N = N,
noccas = 2,
pbeta = logit(c(p1, p2)),
tau = 0, # behavioural effects (i.e. c)
sigma2_zp = 0,
delta_1 = 0.4,
delta_2 = 0.4,
alpha = 0,
data.type = "never",
link = "logit"
)The first few encounter histories under the LR protocol are
[,1] [,2]
[1,] 0 1
[2,] 2 0
[3,] 1 0
[4,] 0 1
[5,] 1 1
[6,] 2 2
[7,] 1 1
[8,] 0 1
[9,] 1 1
[10,] 0 1
We see that encounter matrix has capture histories with 1 representing a L capture and a 2 representing a R capture.
The reduced set of capture histories is:
test.ch <- as.data.frame(test$Enc.Mat)
test.ch.red <- plyr::ddply(test.ch,c("V1","V2"), plyr::summarize,
cap_hist=paste0(V1[1],V2[1]),
freq=length(V1))
test.ch.red V1 V2 cap_hist freq
1 0 1 01 1475
2 0 2 02 1453
3 1 0 10 899
4 1 1 11 631
5 2 0 20 900
6 2 2 22 621
Notice that \(\delta_B = 1-\delta_1-\delta_2 = 0.2\) so for 20% of animals encountered at a sampling event, both the left and right are photographed, but you are unable to link those two photographs together (e.g. taken by different individuals). This implies that the total number of encounters is MORE than expected from the values of \(p_1\) and \(p_2\) by themselves:
Number of pictures of animals at t=1 3051 vs. expected number of 2500
Number of pictures of animals at t=1 4180 vs. expected number of 3500
There evidently some animals detected on both sides, but photos could not be matched. The simulation function also returns the actual encounter history matrix (not shown) that show that some animals are detected on both sides, but could not be matched across the two photographs.
We can get estimates of abundance based on the left or right photos individually in the same way as shown in this document.
For example, based on the left side photographs, the capture history matrix and frequency counts are:
V1 V2 cap_hist freq
1 0 1 01 1475
3 1 0 10 899
4 1 1 11 631
n1 n2 m2 p.recap mf
1 1530 2106 631 0.4124183 0.2996201
This gives the estimate of abundance that is consistent, but estimates of catchability that are confounded with the \(\delta\) values.
left.fit <- Petersen::LP_fit(temp, p_model=~..time)
left.est <- Petersen::LP_est(left.fit)
left.est$summary[, c("N_hat","N_hat_SE","N_hat_conf_level","N_hat_LCL","N_hat_UCL")] N_hat N_hat_SE N_hat_conf_level N_hat_LCL N_hat_UCL
1 5106.467 130.4088 0.95 4857.162 5368.568
left.est$detail$data.expand[1:2,c("..time","p")] ..time p
1 1 0.2996200
1.1 2 0.4124183
Similarly, the capture histories and estimated abundance based on the right side photographs is found as:
temp <- test.ch.red[grepl('2', test.ch.red$cap_hist),]
temp$cap_hist <- gsub('2','1',temp$cap_hist)
temp V1 V2 cap_hist freq
2 0 2 01 1453
5 2 0 10 900
6 2 2 11 621
Petersen::LP_summary_stats(temp) n1 n2 m2 p.recap mf
1 1521 2074 621 0.408284 0.2994214
right.fit <- Petersen::LP_fit(temp, p_model=~..time)
right.est <- Petersen::LP_est(right.fit)
right.est$summary[, c("N_hat","N_hat_SE","N_hat_conf_level","N_hat_LCL","N_hat_UCL")] N_hat N_hat_SE N_hat_conf_level N_hat_LCL N_hat_UCL
1 5079.794 131.2457 0.95 4828.962 5343.656
right.est$detail$data.expand[1:2,c("..time","p")] ..time p
2 1 0.2994217
2.1 2 0.4082842
A naive estimate that combines the two estimates is a simple average with a SE assuming (incorrectly) that these estimates are independent is:
# naive simple average
naive.N.avg <- (left.est$summary$N_hat + right.est$summary$N_hat)/2
cat("Naive estimate of abundance based on simple average ", round(naive.N.avg), "\n")Naive estimate of abundance based on simple average 5093
naive.N.avg.se <- sqrt((left.est$summary$N_hat_SE^2 + right.est$summary$N_hat_SE^2)/4)
cat("Naive SE of average is ", round(naive.N.avg.se), "\n")Naive SE of average is 93
We now use multimark to estimate abundance based on the left and right photographs combined. A model that allows for different capture probabilities at each sampling event is fit by setting up a design matrix. The multimark packages does a Bayesian analysis and so you must specify the number of MCMC iterations to perform etc. The fitting function fits multiple chains in parallel using multiple cores in your machine.
# use multimark to estimate abundance
# we set up my own design matrix, because mod.p=~time creates a design matrix
# that has 3 columns rather than only 2
myCovs <- data.frame(mytime=c(0,1))
myCovs mytime
1 0
2 1
max.iter <- 100000
n.thin <- 10
multimark.res <- file.path("Images","multimark-sim-LR.Rdata")
if( file.exists(multimark.res)){
load(multimark.res)
}
if(!file.exists(multimark.res)){
fit <- multimark::multimarkClosed(
test$Enc.Mat,
data.type = "never",
covs = myCovs,
mms = NULL,
mod.p = ~mytime,
mod.delta = ~type,
parms = c("pbeta", "delta", "N"),
nchains = 3,
iter = max.iter,
adapt = 10000,
bin = 50,
thin = n.thin,
burnin = 2000)
save(fit, file=multimark.res)
}A summary of the MCMC output is:
summary(fit$mcmc)
Iterations = 2010:1e+05
Thinning interval = 10
Number of chains = 3
Sample size per chain = 9800
1. Empirical mean and standard deviation for each variable,
plus standard error of the mean:
Mean SD Naive SE Time-series SE
pbeta[(Intercept)] 0.4077 5.817e-02 3.393e-04 0.0042681
pbeta[mytime] 1.1306 8.011e-02 4.672e-04 0.0051688
N 5065.2233 1.031e+02 6.013e-01 8.6828559
delta_1 0.5010 6.404e-03 3.735e-05 0.0002343
delta_2 0.4953 6.438e-03 3.755e-05 0.0002414
2. Quantiles for each variable:
2.5% 25% 50% 75% 97.5%
pbeta[(Intercept)] 0.2948 0.3672 0.4081 0.4485 0.5191
pbeta[mytime] 0.9828 1.0742 1.1278 1.1846 1.2924
N 4877.0000 4992.0000 5060.0000 5135.0000 5276.0000
delta_1 0.4883 0.4967 0.5011 0.5054 0.5134
delta_2 0.4824 0.4910 0.4953 0.4997 0.5077
# get the estimates of p and c
pc <- multimark::getprobsClosed(fit, link = "logit")
summary(pc)
Iterations = 2010:1e+05
Thinning interval = 10
Number of chains = 3
Sample size per chain = 9800
1. Empirical mean and standard deviation for each variable,
plus standard error of the mean:
Mean SD Naive SE Time-series SE
p[1] 0.6005 0.01395 8.134e-05 0.001023
p[2] 0.8225 0.01756 1.024e-04 0.001430
c[2] 0.8225 0.01756 1.024e-04 0.001430
2. Quantiles for each variable:
2.5% 25% 50% 75% 97.5%
p[1] 0.5732 0.5908 0.6006 0.6103 0.6269
p[2] 0.7881 0.8102 0.8227 0.8352 0.8552
c[2] 0.7881 0.8102 0.8227 0.8352 0.8552
We see that the estimate of abundance appears to be unbiased and has comparable uncertainty to our naive average of estimates of abundance based on the left or right photo individually.
But the estimates of catchability and \(\delta\) are severely biased. Notice that \(\delta_1\) and \(\delta_2\) move towards 0.5 based on the prior distribution for these parameters. Consequently because \(\delta_1\) is overestimated, \(1-\delta_1\) is under estimated, and so the estimated capture probabilities are overestimated..
We can look at the diagnostic plots of the MCMC chains:
plot(fit$mcmc, auto.layout=FALSE)Everything appears to be ok, but only the estimates of abundance are sensible, and the estimates of \(p\) or \(\delta\) really have no meaning!
Given these issues of non-identifiability in the case of 2 sampling events, model averaging likely doesn’t make much sense.
It is not clear if these issues of identifiability also affect analyses with more than 2 sampling events, but I suspect that they do. Some careful analysis using multimark will be required. YMMV.
11.3.2 LRB-type surveys
We now generate simulated data but both sides of some animals can be observed (the B capture type). We will again simulate a population of 5000 individuals with different capture probabilities at the two sample times, but equal \(\delta\) values. About 0.20 of animals that are encountered have both sides read.
logit <- function (p){ log(p/(1-p))}
expit <- function(theta){ 1/(1+exp(-theta))}
set.seed(234324)
N= 5000
p1= .5
p2 = .7
test <- multimark::simdataClosed(
N = N,
noccas = 2,
pbeta = logit(c(p1, p2)),
tau = 0, # behavioural effects (i.e. c)
sigma2_zp = 0,
delta_1 = 0.4,
delta_2 = 0.4,
alpha = 0,
data.type = "always", # some animals have both sides read.
link = "logit"
)The first few encounter histories under the LRB protocol are
[,1] [,2]
[1,] 0 1
[2,] 2 0
[3,] 1 0
[4,] 0 1
[5,] 4 1
[6,] 2 2
[7,] 4 1
[8,] 0 4
[9,] 4 1
[10,] 2 4
We see that encounter matrix has capture histories with 1 representing a L capture and a 2 representing a R capture. A capture history with a 4 represents an animal that has both sides read.
The reduced set of capture histories is:
test.ch <- as.data.frame(test$Enc.Mat)
test.ch.red <- plyr::ddply(test.ch,c("V1","V2"), plyr::summarize,
cap_hist=paste0(V1[1],V2[1]),
freq=length(V1))
test.ch.red V1 V2 cap_hist freq
1 0 1 01 993
2 0 2 02 972
3 0 4 04 351
4 1 0 10 582
5 1 1 11 275
6 1 4 14 130
7 2 0 20 596
8 2 2 22 251
9 2 4 24 131
10 4 0 40 154
11 4 1 41 150
12 4 2 42 163
13 4 4 44 76
Notice that \(\delta_B = 1-\delta_1-\delta_2 = 0.2\) so for 20% of animals encountered at a sampling event, both the left and right are photographed and the two sides can be linked. Some animals with both sides linked are also seen only on the left or right side.
Unlike before, this implies that the total number of encounters is roughly equal to that expected from the values of \(p_1\) and \(p_2\) by themselves because any animal that has both sides captures has them linked.
Number of pictures of animals at t=1 2508 vs. expected number of 2500
Number of pictures of animals at t=1 3492 vs. expected number of 3500
Now any animal that has both sides photographed has them linked.
We can get estimates of abundance based on the left or right photos individually in the same way as shown in this document. We note that type 4 encounters are used in both the left and right sides estimates.
For example, based on the left side photographs, the capture history matrix and frequency counts are:
V1 V2 cap_hist freq
1 0 1 01 993
3 0 4 01 351
4 1 0 10 582
5 1 1 11 275
6 1 4 11 130
9 2 4 01 131
10 4 0 10 154
11 4 1 11 150
12 4 2 10 163
13 4 4 11 76
n1 n2 m2 p.recap mf
1 1530 2106 631 0.4124183 0.2996201
This gives the estimate of abundance that is consistent, but estimates of catchability that are confounded with the \(\delta\) values.
left.fit <- Petersen::LP_fit(temp, p_model=~..time)
left.est <- Petersen::LP_est(left.fit)
left.est$summary[, c("N_hat","N_hat_SE","N_hat_conf_level","N_hat_LCL","N_hat_UCL")] N_hat N_hat_SE N_hat_conf_level N_hat_LCL N_hat_UCL
1 5106.467 130.4088 0.95 4857.162 5368.568
left.est$detail$data.expand[1:2,c("..time","p")] ..time p
1 1 0.2996200
1.1 2 0.4124183
Similarly, the capture histories and estimated abundance based on the right side photographs is found as:
temp <- test.ch.red
temp$cap_hist <- gsub('4','2',temp$cap_hist)
temp$cap_hist <- gsub('1','0',temp$cap_hist)
temp$cap_hist <- gsub('2','1',temp$cap_hist)
temp <- temp[grepl('1', temp$cap_hist),]
temp V1 V2 cap_hist freq
2 0 2 01 972
3 0 4 01 351
6 1 4 01 130
7 2 0 10 596
8 2 2 11 251
9 2 4 11 131
10 4 0 10 154
11 4 1 10 150
12 4 2 11 163
13 4 4 11 76
Petersen::LP_summary_stats(temp) n1 n2 m2 p.recap mf
1 1521 2074 621 0.408284 0.2994214
right.fit <- Petersen::LP_fit(temp, p_model=~..time)
right.est <- Petersen::LP_est(right.fit)
right.est$summary[, c("N_hat","N_hat_SE","N_hat_conf_level","N_hat_LCL","N_hat_UCL")] N_hat N_hat_SE N_hat_conf_level N_hat_LCL N_hat_UCL
1 5079.794 131.2457 0.95 4828.962 5343.656
right.est$detail$data.expand[1:2,c("..time","p")] ..time p
2 1 0.2994217
2.1 2 0.4082842
A naive estimate that combines the two estimates is a simple average with a SE assuming (incorrectly) that these estimates are independent (which is incorrect because some animals are involved in both estimates) is:
# naive simple average
naive.N.avg <- (left.est$summary$N_hat + right.est$summary$N_hat)/2
cat("Naive estimate of abundance based on simple average ", round(naive.N.avg), "\n")Naive estimate of abundance based on simple average 5093
naive.N.avg.se <- sqrt((left.est$summary$N_hat_SE^2 + right.est$summary$N_hat_SE^2)/4)
cat("Naive SE of average is ", round(naive.N.avg.se), "\n")Naive SE of average is 93
We now use multimark to estimate abundance based on the left and right photographs combined. A model that allows for different capture probabilities at each sampling event is fit by setting up a design matrix. The multimark packages does a Bayesian analysis and so you must specify the number of MCMC iterations to perform etc. The fitting function fits multiple chains in parallel using multiple cores in your machine.
# use multimark to estimate abundance
# we set up my own design matrix, because mod.p=~time creates a design matrix
# that has 3 columns rather than only 2
myCovs <- data.frame(mytime=c(0,1))
myCovs mytime
1 0
2 1
max.iter <- 100000
n.thin <- 10
multimark.res <- file.path("Images","multimark-sim-LRB.Rdata")
if( file.exists(multimark.res)){
load(multimark.res)
}
if(!file.exists(multimark.res)){
fit <- multimark::multimarkClosed(
test$Enc.Mat,
data.type = "always",
covs = myCovs,
mms = NULL,
mod.p = ~mytime,
mod.delta = ~type,
parms = c("pbeta", "delta", "N"),
nchains = 3,
iter = max.iter,
adapt = 10000,
bin = 50,
thin = n.thin,
burnin = 2000)
save(fit, file=multimark.res)
}A summary of the MCMC output is:
summary(fit$mcmc)
Iterations = 2010:1e+05
Thinning interval = 10
Number of chains = 3
Sample size per chain = 9800
1. Empirical mean and standard deviation for each variable,
plus standard error of the mean:
Mean SD Naive SE Time-series SE
pbeta[(Intercept)] -0.01547 0.043726 2.550e-04 7.549e-04
pbeta[mytime] 0.81855 0.046360 2.704e-04 4.898e-04
N 5057.90820 85.525972 4.988e-01 1.798e+00
delta_1 0.40083 0.006339 3.697e-05 3.697e-05
delta_2 0.39397 0.006316 3.683e-05 3.665e-05
2. Quantiles for each variable:
2.5% 25% 50% 75% 97.5%
pbeta[(Intercept)] -0.1012 -0.04517 -0.01525 1.393e-02 7.082e-02
pbeta[mytime] 0.7287 0.78716 0.81828 8.493e-01 9.105e-01
N 4895.0000 4999.00000 5057.00000 5.114e+03 5.228e+03
delta_1 0.3884 0.39657 0.40083 4.051e-01 4.133e-01
delta_2 0.3817 0.38971 0.39392 3.982e-01 4.063e-01
# get the estimates of p and c
pc <- multimark::getprobsClosed(fit, link = "logit")
summary(pc)
Iterations = 2010:1e+05
Thinning interval = 10
Number of chains = 3
Sample size per chain = 9800
1. Empirical mean and standard deviation for each variable,
plus standard error of the mean:
Mean SD Naive SE Time-series SE
p[1] 0.4961 0.01093 6.372e-05 0.0001886
p[2] 0.6905 0.01335 7.787e-05 0.0002506
c[2] 0.6905 0.01335 7.787e-05 0.0002506
2. Quantiles for each variable:
2.5% 25% 50% 75% 97.5%
p[1] 0.4747 0.4887 0.4962 0.5035 0.5177
p[2] 0.6645 0.6815 0.6904 0.6995 0.7164
c[2] 0.6645 0.6815 0.6904 0.6995 0.7164
We see that the estimate of abundance appears to be unbiased and has comparable uncertainty to our naive average of estimates of abundance based on the left or right photo individually.
But now with the LRB study design, estimates of catchability and the delta’s are not unbiased.
The MCMC diagnostic plots look fine (but are not shown here)
YMMV.
11.4 Bobcat example
The multimark package also ships with a sample dataset on a study of bobcats. Images of the left and right side were captured using camera traps in 8 sampling locations. It is not possible to match left and right photographs of the bobcats.
The first few records, with one line per photograph are:
# Get the bobcat data
data("bobcat")
head(bobcat) occ1 occ2 occ3 occ4 occ5 occ6 occ7 occ8
ID2 0 0 0 0 0 1 1 0
ID3 0 0 1 0 1 0 0 0
ID4 0 0 0 0 1 0 0 0
ID6 1 0 0 0 0 0 0 0
ID7 0 0 1 0 0 0 0 1
ID8 0 1 0 0 0 0 0 0
The data are very sparse.
We collapse the first 4 sampling occasions into the first “event”, and the last for sampling occasions into the second “event”. In most cases, the photo was only seen once in each of the 4 sets of occasions.
The reduced capture events are shown at the right of each line below:
# classify into 2 events; first 4 sampling events;
# last 4 sampling events; if seen in any of the multiple occasions in an event
bobcat <- cbind(bobcat, V1=apply(bobcat[,c("occ1","occ2","occ3","occ4")],1,max))
bobcat <- cbind(bobcat, V2=apply(bobcat[,c("occ5","occ6","occ7","occ8")],1,max))
head(bobcat) occ1 occ2 occ3 occ4 occ5 occ6 occ7 occ8 V1 V2
ID2 0 0 0 0 0 1 1 0 0 1
ID3 0 0 1 0 1 0 0 0 1 1
ID4 0 0 0 0 1 0 0 0 0 1
ID6 1 0 0 0 0 0 0 0 1 0
ID7 0 0 1 0 0 0 0 1 1 1
ID8 0 1 0 0 0 0 0 0 1 0
This gives us a set of capture histories:
V1 V2 cap_hist freq
1 0 1 01 11
2 0 2 02 13
3 1 0 10 6
4 1 1 11 6
5 2 0 20 6
6 2 2 22 4
The estimated abundances from the left and right sided photographs are:
Left sided abundance estimates
N_hat N_hat_SE N_hat_conf_level N_hat_LCL N_hat_UCL
1 33.99992 7.895085 0.95 21.56856 53.59626
Right sided abundance estimates
N_hat N_hat_SE N_hat_conf_level N_hat_LCL N_hat_UCL
1 42.5 14.39401 0.95 21.88275 82.54221
Naive estimate of abundance based on simple average 38.2
Naive SE of average is 8.2
We now use multimark on the reduced capture histories:
# we set up my own design matrix, because mod.p=~time creates a
# design matrix that has 3 columns rather than only 2
myCovs <- data.frame(mytime=c(0,1))
#myCovs
max.iter <- 100000
n.thin <- 10
multimark.bobcat.res <- file.path("Images","multimark-bobcat.Rdata")
if( file.exists(multimark.bobcat.res)){
load(multimark.bobcat.res)
}
if(!file.exists(multimark.bobcat.res)){
bobcat.fit <- multimark::multimarkClosed(
as.matrix(bobcat[,c("V1","V2")]),
data.type = "never",
covs = myCovs,
mms = NULL,
mod.p = ~mytime,
mod.delta = ~type,
parms = c("pbeta", "delta", "N"),
nchains = 3,
iter = max.iter,
adapt = 10000,
bin = 50,
thin = n.thin,
burnin = 2000)
save(bobcat.fit, file=multimark.bobcat.res)
}This gives the following results
summary(bobcat.fit$mcmc)
Iterations = 2010:1e+05
Thinning interval = 10
Number of chains = 3
Sample size per chain = 9800
1. Empirical mean and standard deviation for each variable,
plus standard error of the mean:
Mean SD Naive SE Time-series SE
pbeta[(Intercept)] -0.2815 0.5679 0.0033118 0.019788
pbeta[mytime] 0.8428 0.6247 0.0036431 0.016251
N 37.5916 8.8429 0.0515727 0.092755
delta_1 0.2654 0.1382 0.0008059 0.008289
delta_2 0.2151 0.1428 0.0008328 0.008920
2. Quantiles for each variable:
2.5% 25% 50% 75% 97.5%
pbeta[(Intercept)] -1.34656 -0.6682 -0.2990 0.08557 0.8857
pbeta[mytime] -0.21701 0.4203 0.7883 1.19137 2.2800
N 26.00000 32.0000 36.0000 41.00000 60.0000
delta_1 0.05044 0.1512 0.2506 0.37023 0.5403
delta_2 0.01011 0.0916 0.1958 0.32458 0.5009
# get the estimates of p and c
pc <- multimark::getprobsClosed(bobcat.fit, link = "logit")
summary(pc)
Iterations = 2010:1e+05
Thinning interval = 10
Number of chains = 3
Sample size per chain = 9800
1. Empirical mean and standard deviation for each variable,
plus standard error of the mean:
Mean SD Naive SE Time-series SE
p[1] 0.4344 0.1305 0.0007611 0.004585
p[2] 0.6137 0.1690 0.0009855 0.007349
c[2] 0.6137 0.1690 0.0009855 0.007349
2. Quantiles for each variable:
2.5% 25% 50% 75% 97.5%
p[1] 0.2064 0.3389 0.4258 0.5214 0.7080
p[2] 0.2975 0.4894 0.6100 0.7358 0.9357
c[2] 0.2975 0.4894 0.6100 0.7358 0.9357
The estimated abundance is comparable to our naive estimate. It is unclear how the estimates of catchability and for \(\delta\) perform (see previous section).
The diagnostic plots from the MCMC iterations are:
12 Multiple Petersen estimates
12.1 Introduction
In some cases, multiple Petersen experiments occur on study population over a short time period (when the population is assumed closed). For example, 200 fish could be initially marked as they return to their spawning grounds. At a weir, a sample of 1000 fish are taken and the number of tagged fish noted. No additional tags are applied; no tags are removed; and fish are returned to the stream. Then on the spawning ground an additional 1200 fish are sampled of which some are marked.
On the surface, this appears that a closed population model with three sampling occasions could be fit. However, this is not possible because unmarked fish captured at the weir are not tagged and returned to the population. Consequently, no capture histories can be constructed for fish first captured at the weir and released. If individually identifiable tags are used, then a capture-history could be constructed for tagged fish; but if batch marks are used, then this is also not possible because it is impossible to determine if an untagged fish is captured at the weir and then again on the spawning grounds. Finally, it sometimes occurs that additional tags are applied to some (but not all untagged fish) captured at the weir and most closed population models cannot deal with the addition of more tags partway through the study.
These types of studies are known as mark-resight models (McClintock et al., 2009; McClintock and White, 2012). There are many previous estimators for this situation - refer to McClintock and White (2012) for details - but modern approaches use the likelihood based estimators where the probability of recapture varies among the sampling occasions, the population is closed, and the number of marks available is known for each sampling occasion. McClintock et al (2012) indicated that the logit-normal estimator should only be used with sampling is without replacement so that an animal can only be recaptured a maximum of one time, and the Poisson-log-normal estimator should be used if sampling occurs with replacement, i.e., captured-fish are returned to the study population. However, the latter model will require individually-identifiable tags so that the number of times a tagged-fish is recaptured is known. If batch marks are used and the sampling fractions are small, the logit-normal estimator will provide a close approximation.
McClintock and White (2012) provide a summary of the conditions under which these two (and a third) estimators can be used in Table 33.
| Estimator | Geographic closure | Sampling with replacement | Known number of marks | Identifiable marks |
|---|---|---|---|---|
| LNE | Required | Not allowed | Required | Not required |
| PNE | Required | Allowed | Not required | Required |
| IELNE | Not required | No allowed | Required | Not required |
The IELNE allows for non-closure of the population (e.g., new animals entering the population), but is not discussed here.
Note that close approximation to the LNE estimator can be obtained by pooling all of the subsequent samples (assuming that the number of marks has not changed), and treating the weir and spawning group samples like a single “larger” recapture event. Duplicate recaptures of marked or unmarked fish are treated as two separate recaptures.
There easiest way to use these models is via RMark/MARK as shown below for the LNE model. The PNE model is specified similarly, but requires individually-marked fish.
12.2 Batch marks (logit-normal model)
This model is suitable for batch marks where a capture-history cannot be determined for individual animals. It assumes that sampling is without replacement, but as long as the number of animals sampled is small relative to the population size, the estimator should perform well.
We consider a study where salmon enter a stream and are marked. Two sample are taken upstream, at a weir and on the spawning grounds as summarized in Table 34.
| Event | Marks available | Recapture size | Marks seen | Petersen Est |
|---|---|---|---|---|
| \(n_1\) | \(n_2\) | \(m_2\) | ||
| 1 | 200 | 1027 | 18 | 10,874 |
| 2 | 200 | 1305 | 26 | 9,721 |
We first create the capture-history file with pseudo-histories for the tagged fish ignoring the first capture event where 200 marks are applied.
data_salmon <- data.frame(
ch= c("10", "01", "00"),
freq=c( 18, 26, 200-18-26)
)
data_salmon ch freq
1 10 18
2 01 26
3 00 156
Notice the first two rows report the number of marks seen at each sampling event. The last history (“00”) is technically unobservable and is a “dummy” history to represent the number of marks originally applied and never seen. Again, we are assuming that the sample sizes are small relative to the population sizes that sampling without replacement is a suitable approximation. The rule needed to create the histories is that the sum of the 1’s in a column x the count must equal the number of marks seen. There are several ways in which the histories can be constructed. The above histories are more easily interpreted if a “1” is temporarily prepended to each history for the marking event.
A . (period) can be used if the number of marks varies among the sampling events (e.g. marks added between event or marks lost between events). The following capture_history file has the same number of recaptures, but 10 marked fish were lost after sampling at the weir due to the proximity of a BBQ. Consequently, the number of marks available is 200 and 190 for the two future sampling events.
data_salmon2 <- data.frame(
ch= c("10", "01", "0.", "00"),
freq=c( 18, 26, 10, 200-18-26-10)
)
data_salmon2 ch freq
1 10 18
2 01 26
3 0. 10
4 00 146
Now there are \(200-18-26-10=146\) marked fish not seen at both sampling occasions, with an additional 10 fish not seen at the first subsequent sampling occasion, but not available for the second subsequent sampling event. Again, prepend a “1” in front of each history to interpret the histories more readily. Histories can be constructed for adding new marks as well.
We launch RMark and see which parameters must be specified for this model:
library(RMark)
setup.parameters("LogitNormalMR", check=TRUE) [1] "p" "sigma" "N"
The parameter
- \(p\) represents the mean (logit) capture probability;
- \(sigma\) represent variation in the (logit) capture probability over individuals. Because we don’t have individually marked fish, we must set this parameter to 0 for this example.
- \(N\) represents the population abundance.
We need to use the process.data() function to specify the umber of unmarked fish seen in the experiment:
salmon.proc <- process.data(data_salmon,model="LogitNormalMR",
counts=list("Unmarked seen"=c(2288)),
time.intervals=c(0))
salmon.ddl <- make.design.data(salmon.proc)The time intervals of 0 indicate a single session (i.e. year) of data where the population is assume closed with two secondary sessions in this single primary session. The make.design.data() function creates the analysis structure.
Specify a model in the usual way using RMark We will start with a p(t), sigma=0 model.
Due to a ‘feature’ in MARK when called by RMark, poor initial values are chosen and the model converges to nonsense. We need to create sensible initial values on the beta scale. For the capture probabilities (the logit scale), we can use the value of 0 (once for each occasion), for the sigma parameter, we are initializing and fixing at 0 and for the abundance (N), we use log(approximate abundance). Here the approximate abundance is about 10,000 so we use log(10,000).
salmon.mt <- mark( salmon.proc,
model="LogitNormalMR",
model.name="(p(t) sigma=0)",
model.parameters=
list(p =list(formula=~time),
sigma=list(formula=~1, fixed=0),
N =list(formula=~1)),
initial=c(0,0,0,log(10000))
)
Output summary for LogitNormalMR model
Name : (p(t) sigma=0)
Npar : 3
-2lnL: 285.0223
AICc : 291.0828
Beta
estimate se lcl ucl
p:(Intercept) -2.3127836 0.2472701 -2.7974329 -1.828134
p:time2 0.4137078 0.3248364 -0.2229716 1.050387
N:(Intercept) 9.2480824 0.1432740 8.9672654 9.528899
Real Parameter p
Session:1
1 2
0.0900698 0.1302131
Real Parameter sigma
Session:1
0
NA
Real Parameter N
Session:1
10584.63
salmon.mt$results$real estimate se lcl ucl fixed
p g1 s1 t1 9.006980e-02 0.0202656 0.0574631 1.384607e-01
p g1 s1 t2 1.302131e-01 0.0238270 0.0901817 1.844126e-01
N g1 s1 1.058463e+04 1487.8476000 8053.3129000 1.393186e+04
sigma g1 a0 s1 t0 0.000000e+00 0.0000000 0.0000000 0.000000e+00 Fixed
note
p g1 s1 t1
p g1 s1 t2
N g1 s1
sigma g1 a0 s1 t0
The estimated abundance is
get.real(salmon.mt, "N", se=TRUE) all.diff.index par.index estimate se lcl ucl fixed note
N g1 s1 4 3 10584.63 1487.848 8053.313 13931.86
group session
N g1 s1 1 1
We can fit a model where the capture probabilities are equal across both subsequent sampling events:
salmon.m0 <- mark( salmon.proc,
model="LogitNormalMR",
model.name="(p(.) sigma=0)",
model.parameters=
list(p =list(formula=~1),
sigma=list(formula=~1, fixed=0),
N =list(formula=~1)),
initial=c(0,0,log(10000)) )
Output summary for LogitNormalMR model
Name : (p(.) sigma=0)
Npar : 2
-2lnL: 286.6689
AICc : 290.699
Beta
estimate se lcl ucl
p:(Intercept) -2.089332 0.1598152 -2.402570 -1.776095
N:(Intercept) 9.248113 0.1435710 8.966714 9.529512
Real Parameter p
Session:1
1 2
0.110138 0.110138
Real Parameter sigma
Session:1
0
NA
Real Parameter N
Session:1
10584.95
salmon.m0$results$real estimate se lcl ucl fixed
p g1 s1 t1 0.110138 0.0156631 0.0829769 0.144786
N g1 s1 10584.951000 1490.9778000 8049.0515000 13940.158000
sigma g1 a0 s1 t0 0.000000 0.0000000 0.0000000 0.000000 Fixed
note
p g1 s1 t1
N g1 s1
sigma g1 a0 s1 t0
The model comparison table is constructed in the usual way.
salmon.modset <- collect.models( type="LogitNormalMR")
salmon.modset model npar AICc DeltaAICc weight Deviance
1 (p(.) sigma=0) 2 290.6990 0.0000000 0.5478212 286.6689
2 (p(t) sigma=0) 3 291.0828 0.3837426 0.4521788 285.0223
You CANNOT use the standard model.average() function due to the way MARK and RMark interact (groan)! Notice that the model averaged estimate is \(N\) is WRONG.
salmonavg.N.wrong <- model.average(salmon.modset, parameter="N", vcv=TRUE) # WRONG ANSWER
salmonavg.N.wrong$estimates
par.index estimate se lcl ucl fixed note group session
N g1 s1 4 10384.81 1489.563 7839.795 13755.99 1 1
$vcv.real
4
4 2218798
The model averaged value of \(N\) is lower than each of the estimates which is impossible because it actually extracts the estimated UNMARKED population abundance from each subsequent capture event (groan).
You need to create a list structure to use model.average.list() function – see the help file on this function.
est.list <- function(modset){
# Extract the estimate, AICc, and SE from the model sets
# we need list with three vectors
estimate <- plyr::laply(modset[ names(modset) != "model.table"],
function(x){get.real(x, "N", se=TRUE)$estimate})
weight <- modset$model.table$weight
se <- plyr::laply(modset[ names(modset) != "model.table"],
function(x){get.real(x, "N", se=TRUE)$se})
list(estimate=estimate, weight=weight, se=se)
}
est.to.average <- est.list(salmon.modset)
est.to.average$estimate
[1] 10584.95 10584.63
$weight
[1] 0.5478212 0.4521788
$se
[1] 1490.978 1487.848
This creates a list with 3 vectors corresponding to the estimates to be averaged, the weights for the estimates, and the SE of the individual model estimates.
Finally, we can model average using this data structure (groan):
salmonavg.N <- model.average(est.to.average, mata=TRUE) # mata argument request ci's
salmonavg.N$estimate
[1] 10584.81
$se
[1] 1489.563
$lcl
[1] 7665.316
$ucl
[1] 13504.3
[1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
This procedure is not for the faint of heart!
- Capture histories are “imaginary” and are devices to getting the information into MARK. In particular the use of the 00 and 0. histories to allow for marks to be added and removed is not intuitive.
- The total count of unmarked animals is specified in the process.data() function.
- Need to specify good starting values on the beta (logit or log scale depending on the parameter) scale (groan)!
- Cannot use the standard model.average() function and need to use the model.average.list() function (groan).
As a point of interest, the pairs of Petersen estimates formed at the second and third sampling event and by pooling the subsequent capture events are shown in Table 35.
| Events | Estimate | SE |
|---|---|---|
| 1 & 2 | 10,874 | 2292 |
| 1 & 3 | 9,721 | 1692 |
| Average | 10,297 | ???? |
| Pooled | 10,420 | 1340 |
12.3 Example of PNE method - TBA
12.4 Summary
13 Forward and reverse capture-recapture studies
13.1 Introduction
Consider a capture-recapture study of fish returning to spawn that consists of many distinct stocks with different spawning grounds.
In a forward capture-recapture recapture study, fish are captured at the entrance to the river, tagged and released. Then on one particular spawning ground, fish are examined for tags. But in many cases, biological samples are taken are also taken when fish are tagged, and genetic methods used to estimate the stock proportions.
This can be used in “reverse” capture-recapture study. If fish are fully enumerated on the spawning ground (e.g., at a fence), this is considered the “tagging” event. Then working backward, the biological samples are the “recapture” event.
This methodology is explained in more detail in Hamazaki and DeCovich (2014). The key assumptions for the genetic reverse-capture-recapture method (in addition to the usual for a Petersen estimator) include:
- Complete enumeration of stock on the spawning ground or at a weir. A complete enumeration of the stock is needed to ensure that the “tagging” event is complete. This assumption could be violated by the stock spawning elsewhere (e.g., main stem), or not all spawning areas surveyed. Or multiple stocks with different genetic baselines could spawn in the same spawning grounds.
- The genetic baseline is complete and accurate. The baseline needs to be complete in-order to confidently assign individuals to the “marked” (genetically distinct) population. If incomplete, individuals from genetically similar populations may be assigned to the “marked” population (see below) because it is the “closest” populations for assignment. This assumption can be relaxed if “not in baseline” is an acceptable assignment for stocks not in the baseline. The genetic baseline must also be accurate, e.g., fish the form the baseline really belong to the stock of interest and are not a mixture of multiple stocks.
- Marked population is genetically distinct. The identified “marked” population needs to be genetically distinct from all other populations in the system so that individuals from genetically similar populations are not assigned to the “marked” population introducing bias in the estimated proportion of the “marked” population during the “second” sampling occasion at the entrance to the system.
- Marked population size. While the size of the “marked population” theoretically has no bearing on the estimator, a small stock may have too few “recaptures” in the biological samples and so the estimator may have very poor precision.
- Equal en route mortality among different components of the run. En route morality in the reverse capture-recapture method acts like “immigration” in the forward capture-recapture methods and so leads to valid estimates at the entrance to the system. Homogeneous en route mortality may be violated when there are differential stock-specific harvest rates among stocks. This assumption can be assessed in the harvest through rigorous tissue collection of harvested individuals. The assumption may also be violated if stock have different distances between the entrance to the system and their spawning sites and so the en route mortality may also differ. One way to test this assumption is via the goodness of fit testing of equal recovery probabilities discussed earlier.
- Random sampling at the entry to the system. Random sampling at the entry to the system could occur if, for example, fishwheels are sampling approximately proportional to the run and a constant fraction of the tagged fish have biological samples taken, e.g., every nth tagged fish is sampled.
13.2 Example - Run size of Yukon River Chinook
This is the 2011 data from Hamazaki and DeCovich (2014) taken from Table 2 of their paper.
Briefly, Chinook Salmon returning to Yukon River are counted in the lower river (Pilot Station) using hydroacoustic and sonar methods. At the same time, biological samples are taken throughout the run and the stock of origin was determined using GSI methods. In particular, in 2011, the proportion of stocks of Canadian origin was 0.35 (SE .030) based on a sample size of 251 fish of which 87 were fish of Canadian origin.
Fish continue their upward migration and the number of fish that enter Canadian waters was counted using sonar at the Eagle Border Station (51,271 (SE 135)). To this was added the estimated harvest of Canadian fish between Pilot Station and Eagle Border Station from harvest monitoring given a total of 66,225 (SE 1514) Canadian fish. These are considered to be the “tagged” fish.
Now consider running the experiment in reverse. We have 66,225 are marked at Eagle Border and swim “backwards” to Pilot Station. Here a biological sample of 251 fish were extracted, of which 87 were fish from Canada. This is the “recapture” sample. So, in reverse, we have \(n_1=66,225\); \(n_2=251\), \(m_2=87\) giving a reverse Petersen estimate of \[\widehat{N}_{reverse}=\frac{n_1 \times n_2}{m_2}=\frac{66,225 \times 251}{87}=191,062\] as reported in their paper. [Their estimate is slightly different because of rounding.]
The data are available in the Petersen package:
data(data_yukon_reverse)
data_yukon_reverse cap_hist freq se
1 10 66138 1574.00000
2 11 87 7.53865
3 01 164 0.00000
comment
1 Escapement + harvest - genetic samples recaptured cdn fish
2 Genetic sample that are cdn fish
3 Genetic sample that are non-cdn fish
The estimates are obtained in the usual way:
yukon.fit <- Petersen::LP_fit(data_yukon_reverse,
p_model=~..time)
yukon.est <- Petersen::LP_est(yukon.fit, N_hat=~1)
yukon.est$summary N_hat_f N_hat_rn N_hat N_hat_SE N_hat_conf_level N_hat_conf_method
1 ~1 (Intercept) 191062.9 16546.88 0.95 logN
N_hat_LCL N_hat_UCL p_model name_model cond.ll n.parms nobs method
1 161234.7 226409.2 ~..time p: ~..time -1812.538 2 66389 CondLik
The reported SE is too small because it does not account for the uncertainty in the \(n_1\) (uncertainty in harvest and from sonar) and \(m_2\) (because genetic assignment has some error). The LP_est_adjust() function can again be used. First, we get the adjustment factors for \(n_1\) and \(m_2\) based on the reported uncertainties:
n1.adjust.est <- 1
n1.adjust.se <- data_yukon_reverse$se[ data_yukon_reverse$cap_hist=="10"] / data_yukon_reverse$freq[ data_yukon_reverse$cap_hist=="10"]
cat("Estimated adjustment factors for n1 ", n1.adjust.est, n1.adjust.se, "\n")Estimated adjustment factors for n1 1 0.02379872
m2.adjust.est <- 1
m2.adjust.se <- data_yukon_reverse$se[ data_yukon_reverse$cap_hist=="11"] / sum(data_yukon_reverse$freq[ data_yukon_reverse$cap_hist!="10"])
cat("Estimated adjustment factors for m2 ", m2.adjust.est, m2.adjust.se, "\n")Estimated adjustment factors for m2 1 0.03003446
And, now the adjustment factors are applied
set.seed(34543534)
yukon.adjust <- LP_est_adjust(
yukon.est$summary$N_hat, yukon.est$summary$N_hat_SE,
n1.adjust.est=n1.adjust.est, n1.adjust.se=n1.adjust.se,
m2.adjust.est=m2.adjust.est, m2.adjust.se=m2.adjust.se
)
yukon.adjust$summary N_hat_un N_hat_un_SE N_hat_adj N_hat_adj_SE N_hat_adj_LCL N_hat_adj_UCL
1 191062.9 16546.88 191996.4 18417.44 158396.5 230678
The final answer matches those reported in the paper (\(\widehat{N}_{paper}=191,155\) (SE \(18,372\))) where the authors used a bootstrapping procedure (similar to that used in the LP_est_adjust() function).
13.3 Example: Lower Fraser Coho - SPAS in reverse
This example was provided by Kaitlyn Dionne from the Department of Fisheries and Oceans, Canada and is discussed in Arbeider et al (2020) in more detail.
Arbeider et al (2020) proposed to estimate the run size of Lower Fraser River Coho (LFC) using a geographically stratified reverse-capture method. Briefly, as LFC coho swim upstream in the Fraser River, they are sampled near New Westminister, BC, which is downstream from several major rivers with large spawning populations. These sampled fish are assigned to the spawning population using genetic stock identification and other methods. These spawning populations are identified as the Chilliwack Hatchery (denoted C), the Lilloet River natural spawning population (denoted L), the Nicomen Slough population (denote N) and all other populations (denoted as 0). Notice that the sampled fish at New Westminister are NOT physically tagged, and population assignment is through genetic stock identification and other measures.
The upstream migration extends over two months (September to October) and is divided into 3 temporal strata corresponding to Early (denoted 1E), Peak (denoted 2P) and Late (denoted 3L). The digits 1, 2, 3 in front of the codes ensures that the temporal strata are sorted temporally, but this is merely a convenience and does not affect the results.
The spawning populations at C, L, and N are estimated by a variety of methods (see Arbeider, et al. 2020). Each of the population estimates also has an estimated SE (which will be ignored for now).
The data are available in the Petersen package:
data(data_lfc_reverse)
data_lfc_reverse cap_hist freq SE
1 C..1E 23 NA
2 C..2P 44 NA
3 C..3L 6 NA
4 C..0 66127 13039
5 L..1E 12 NA
6 L..2P 8 NA
7 L..3L 2 NA
8 L..0 14300 403
9 N..1E 1 NA
10 N..2P 13 NA
11 N..3L 3 NA
12 N..0 15274 461
13 0..1E 37 NA
14 0..2P 146 NA
15 0..3L 46 NA
This can be displayed in a matrix form as:
s2
s1 0 1E 2P 3L
0 0 37 146 46
C 66127 23 44 6
L 14300 12 8 2
N 15274 1 13 3
The first row (corresponding to s1=0) are the number of fish in the New Westminister sample assigned to stocks other than C, L, or N. The first column (corresponding to s2=0) are the estimated total escapement in each of C, L, N (less the fish removed for genetic identification which are trivially small). The matrix in the lower bottom of the above array shows the number of fish assigned from the New Westminister sample to the four (C, L, N, and 0) geographic strata in each of the 3 time periods (1E, 2P, or 3L).
Notice that this data set up is going in REVERSE from total spawning escapement backwards to the genetic sample in New Westminister.
13.3.1 Fitting the SPAS model
The SPAS model is fit to the above data using the wrapper supplied with this package. We start with no pooling of rows or columns.
mod..1.fit <- Petersen::LP_SPAS_fit(data_lfc_reverse,
model.id="LFC - entire matrix",
row.pool.in=1:3, col.pool.in=1:3,quietly=TRUE)The summary of the fit is:
mod..1.fit$summary p_model name_model cond.ll n.parms nobs method
1 Refer to row.pool/col.pool LFC - entire matrix 923265.5 15 96042 SPAS
cond.factor
1 2095.344
The usual conditional likelihood is presented etc. Of more importance is the condition factor. This indicates how close to singularity the recovery matrix (in this case, the stock assignment of New Westminister fish to the geographic and temporal strata) is with larger values indicating that the matrix of “recoveries” is closer to singularity. Usually, this value should be 1000 or less to avoid numerical issues in the fit. Here the conditional factor is around 2000 which is a bit concerning but still likely to be acceptable.
We also fit a model (not shown) where the first two geographic strata (C and L) were pooled and give essentially the same abundance estimate.
We estimate the total LFC population:
mod..1.est <- Petersen::LP_SPAS_est(mod..1.fit)
mod..1.est$summary N_hat_f N_hat_rn N_hat N_hat_SE N_hat_conf_level N_hat_conf_method
1 NA NA 289861.2 42516.79 0.95 Large sample
N_hat_LCL N_hat_UCL p_model name_model cond.ll
1 206529.8 373192.6 Refer to row.pool/col.pool LFC - entire matrix 923265.5
n.parms nobs method cond.factor
1 15 96042 SPAS 2095.344
The reverse capture-recapture stratified-Petersen estimate of the total number of fish passing the New Westminister sampling station is 289,861 with a standard error of 42,517.
The pooled-Petersen estimator can be obtained by pooling all rows to a single row:
mod..PP.fit <- Petersen::LP_SPAS_fit(data_lfc_reverse, model.id="Pooled Petersen",
row.pool.in=rep(1,3),
col.pool.in=c(1,2,3),quietly=TRUE)
mod..PP.fit$summary p_model name_model cond.ll n.parms nobs method
1 Refer to row.pool/col.pool Pooled Petersen 923258.6 13 96042 SPAS
cond.factor
1 1
mod..PP.est <- Petersen::LP_SPAS_est(mod..PP.fit)
mod..PP.est$summary N_hat_f N_hat_rn N_hat N_hat_SE N_hat_conf_level N_hat_conf_method
1 NA NA 291716.4 22575.55 0.95 Large sample
N_hat_LCL N_hat_UCL p_model name_model cond.ll
1 247469.1 335963.6 Refer to row.pool/col.pool Pooled Petersen 923258.6
n.parms nobs method cond.factor
1 13 96042 SPAS 1
The capture-recapture reverse pooled-Petersen estimate of the total number of fish passing the New Westminister sampling station is 291,716 with a standard error of 22,576, which is virtually identical to the reversed stratified estimate but with a considerably reduced SE.
The above analysis ignored the uncertainty in the estimated escapement and so the reported standard errors for abundance are under reported. An approximate measure of this additional uncertainty for the pooled-Petersen reverse capture-recapture estimate could be obtained by bootstrapping, or using the LP_est_adjust() function.
# get the total of "n1" (reverse) and its approximate SE
temp <- data_lfc_reverse[ grepl("0$", data_lfc_reverse$cap_hist),]
n1 <- sum(temp$freq)
n1.rse <- sqrt(sum(temp$SE^2))/n1
est.adj <- LP_est_adjust(mod..PP.est$summary$N_hat, mod..PP.est$summary$N_hat_SE, n1.adjust.est=1, n1.adjust.se=n1.rse)
est.adj$summary N_hat_un N_hat_un_SE N_hat_adj N_hat_adj_SE N_hat_adj_LCL N_hat_adj_UCL
1 291716.4 22575.55 292894.4 46348.98 205007.6 388175.5
This shows that the uncertainty in the escapement in the terminal run would increase the SE of the abundance estimates by about 50%!
13.4 Example combining forward and reverse capture-recapture studies
TBA
13.5 Summary
The reverse capture-recapture method requires no mortality (either natural or harvest) between the location of the biological sample and the final spawning grounds. Otherwise, these sources of removal must be added to the “tagged” group when applied in reverse.
This is different from the forward capture-recapture experiment where mortality between the tagging and recapture events is allowable if it applies equally to tagged and untagged fish. When running the estimator in reverse, it would appear on first glance that any mortality should have similar effects to immigration where the abundance could still be estimated at the second sampling event. However, the key difference is that immigration in the forward direction applies only to untagged fish, but in the reverse direction mortality (now appearing to be immigration) is being applied to “tagged” fish.
14 Genetic capture-recapture methods using close kin studies
Genetic markers that unique identify individual can used in place of marks or tags and pose no unique challenges. An interesting new application is the use of transgenerational marks where the set of animals sampled are different in the two events.
Single sample methods? Like the sequential capture-recapture methods taking one sample at a time? Rarefaction curves?
14.1 Transgenerational capture-recapture
14.1.1 Introduction
In these studies, The first sample is of adults is captured and a set of genetic markers (e.g., SNPs) are established for each captured animals. These adults mate and reproduce. A second sample of offspring is captured. The genetic information from these offspring is obtained. If the genetic markers are sufficiently diverse, then a parent-offspring-pair may be established in some cases, i.e., for some of the offspring, it can be established if the father and/or mother arose from the initial marked set (Figure 27).
Notice that the set of animals sampled at the two sample events is different. Each juvenile sampled has two “genetic tags” (one for the father and one for the mother). Because a parental pair can give rise to many offspring and mother/father relationships may not be monogamous, multiple juveniles can have the “genetic tag” for a particular adults fish in the original samples.
Rawding et al (2014) used this method to estimate the number of returning Chinook salmon in the Coweeman River, Washington State. The marks were the genotyped carcasses collected from the spawning area during the first sampling event. The second sampling event consisted of a collection of juveniles from a downstream migrant trap located below the spawning area. The parents that assigned to the juveniles through parentage analysis were considered the recaptures, which was a subset of the genotypes captured in the second sample.
Rosenbaum et al (2024) also used a similar method to estimate the number of returning Chinook salmon in the Chilkat River in Alaska State. Returning adult Chinook salmon were captured during freshwater migration in June and July using fishwheels and drift gillnets or in August using rod and reel, dip nets, short tangle nets, beach seines, and carcass surveys. Juvenile tissue samples were collected in the fall of 2021 using a stratified systematic sampling design, with samples collected continuously throughout September and October, across the mainstem and two of the three primary spawning tributaries using baited minnow traps.
In both examples, kinship relationships among adults and juveniles was determined using the parentage analysis program COLONY (Wang & Santure, 2009).
COLONY is a full probability pedigree reconstruction software that uses maximum likelihood to reconstruct full- and half-sibling family groups among juveniles and assigns parents to family groups. Additionally, COLONY infers genotypes of unsampled parents through information of sibling relationships among juveniles. Reconstructing unsampled parental genotypes allows for putative identification of the total number of reproductively successful adults, both sampled and unsampled.
14.1.2 Bailey Binomial model
In the first model, the genetically typed adults are treated as the marked sample, and each juvenile genetically sampled is treated as two (independent) draws from the population of adults. Because a parental pair can produce multiple offspring, the juvenile samples treated as sampling with replacement. These are the conditions suitable for a Bailey (1951, 1952) binomial estimator.
Rosenbaum et al (2024) provided the raw genetic matching data from their study. When processed, this gives rise to the summary data in Table 36:
Capture | Total | Frequency |
|---|---|---|
01 | 1 | 279 |
01 | 2 | 191 |
01 | 3 | 86 |
01 | 4 | 21 |
01 | 5 | 9 |
01 | 6 | 6 |
01 | 7 | 5 |
01 | 9 | 1 |
10 | 0 | 434 |
11 | 1 | 96 |
11 | 2 | 31 |
11 | 3 | 11 |
11 | 4 | 5 |
11 | 5 | 1 |
11 | 6 | 1 |
11 | 7 | 2 |
A total of \(M=\) 581 adults were captured and genotyped (histories 10 and 11 in Table 36). Most were not “recaptured” by the father/mother genotyping of the juveniles, but 96 adults were “recaptured” in the juvenile sample once, 31 adults were captured 2x; etc.
A total of 682 juveniles were genotypes and each gives rise to 2 parental genotypes, some of which are matched, amd 279 juvenile mother/father slots were not recaptures of the adults from previous fall. This gives \(C=\) 1364 (number of juvenile genotypes measured - two from each fish).
Finally, a total of \(R =\) 236 “recaptures” (including double, triple counting etc.) were found.
The (bias adjusted) Bailey Binomial estimate of adults abundance in the fall is \[\widehat{N}_{BB} = \frac{M \times (C+1)}{R+1}\] and found to be 3346 (SE 197) fish.
14.1.3 Hypergeogeometric model
The Bailey Binomial model assumes that on each draw (i.e., each juvenile) has an equal chance of selecting each adult parental genotype. However, a more fecund fish will likely give rise to more juveniles, and so the assumption of equal probability of sampling an adults fish is violated.
For this reason, the number of UNIQUE genotype in the juvenile sample can be used in the usual hypergeometric (Petersen or Chapman) estimator.
The value of \(M\) (number adults genotypes) is unchanged. The number of unique adults recaptured can be derived from Table 36 by treating multiple recaptures of the same adult genotype as single capture event. This give \(R_{unique}\) = 147.
Similarly, the number of unique adult genotypes seen for the first time is also determined from Table 36. For this study this gives \(C_{unique}\) = 745.
This gives an estimate of 2933 (SE 186) fish.
Both estimates are similar.
14.1.4 Caution on using simple sample methods.
It might be tempting to use single-sample methods based on the sample of juveniles alone such as species rarefaction curves, or methods developed for capture-recapture that allow for heterogeneity (such as Chao’s estimate for the lower bound on the number of species). However, these methods will give you an estimate for the number of adults that successfully bred and had juveniles that suvived to the time of sampling. This can be substantially less than the total number of adults that returned to spawn.
For example, Chao’s simple estimator of \[\widehat{N}_{Chao} = C_{unique} + \frac{f_1^2}{2 f_2}\] where \(f_i\) is the number of adult genetic codes captured \(i\) time in the juvenile sample, and \(C_{unique}\) is the number of unique adult genetic codes seen in the juvenile sample gives an estimate of 949 adults, which is substantially less than the other estimates, presumably because of the large number of returning adults who do not breed, nor had juveniles that survived to the time of sampling.
14.1.5 Limitations and Assumptions
The key assumptions needed to ensure that the Petersen (and related) estimators are unbiased are
- there is no mark loss,
- there are no marking effects,
- the population is closed,
- all marked and unmarked fish are correctly identified and enumerated, and
- all fish in the population have an equal probability of capture in at least one sample event, or there is complete mixing of marked and unmarked individuals. There are additional, biologically unlikely, ways.
Genetic-based approaches meet the no tag-loss and no marking-effects assumptions, because genotypes were permanent markers and genetic marks were obtained from adults or from juveniles.
The closure assumption requires that within the study period there are no additions to the population through births or immigration and no deletions through death or emigration. In this studies, the closure assumption is likely violated by adults failing to produce offspring; however, the Petersen estimator is unbiased with respect to the population at time of tagging if mortality was random. Similarly, if the carcass collection was unbiased regarding the production of at least one offspring and the mortality (i.e., lack of spawning success) was equal for sampled and unsampled carcasses. There is likely no a priori reason to believe carcass sampling was not representative relative to the production of at least one offspring.
Regarding juveniles, careful study design is required to ensure that only juveniles from the adults population in the fall are sampled.
Good laboratory procedures and sufficient genetic markers are needed to ensure that correct identification and reporting of tagged or marked fish (assumption 4).
The last assumption (homogeneity of capture probabilities in at least one sample event) is the most difficult to ensure is being met. A representative carcass sampling design can be used to obtain a sample of parents. For tGMR, differences in individual parental reproductive success create unequal capture probabilities for parents in the second sampling event. When repeatedly sampling the same individual, the heterogeneity in capture probabilities can be partially alleviated by using only unique adults captures.
Equal mixing would imply that juveniles produced by the adults marked fish mix completely with the juveniles produced by unmarked adult fish. This could be violated by geographic separation of spawning adults, etc.
Rosenbaum et al (2024) concluded that the binomial tGMR estimate is less robust to assumption violations and more prone to biases as a result of following sampling with replacement. They caution tGMR users from relying on the binomial estimator. Instead, it is preferable to identify an informative panel of genomic markers for the target population to confidently infer unsampled parents during parentage analysis so that the hypergeometric framework may be reliably utilized.
Heterogeneity can be (partially) alleviated through the use of covariates as presented early in this manuscript. However, covariates are readily available for the “marked” sample of adults, but not for the adults never seen before as identified by the juvenile sampling. It may be possible to identify sex by a marker, but other geographic or temporal covariates cannot be assigned to every unique adult seen. This is a major limitation of the use of genetic methods in capture-recapture experiments.
Rosenbaum et al (2024) also present a simulation program to examine the impact of various assumption violations on the estimates. Consult their paper for more details.
Rawding et al (2014) also conclude
The genetic methods we describe can be used with other anadromous salmonids that immigrate to the ocean shortly after emergence, such as Chum Salmon Oncorhynchus keta and Pink Salmon O. gorbuscha. Yet, additional considerations are needed to extend this application to anadromous salmonids with yearling life histories, such as spring Chinook Salmon, Coho Salmon O. kisutch, and Atlantic Salmon Salmo salar. Further, Atlantic Salmon and steelhead O. mykiss produce unique challenges because smolts may be the offspring of anadromous fish or resident fish or both. Using our methods, the Nc and Nb for steelhead would include the combined resident and anadromous spawning population, which may not meet manager needs, as the anadromous life history form is listed for protection under the ESA, while individuals exhibiting a resident life history are not listed.
The tGMR approach could also be extended to estimate adult abundance using only returning adults. Rather than the second sampling event consisting of juvenile captures, the second event would be a capture of returning adults. By aging the scales from returning adults, the adults could be assigned to the appropriate brood year based on scale ages, and tGMR could then be used to estimate spawner abundance for relevant brood years. Another variant of the genetic mark–recapture design is to estimate smolt abundance via “back-calculation” (Volkhardt et al. 2007). In this approach the smolts are the marks and the returning adults are the recaptures and captures.
15 Grand summary
The Petersen estimator is the simplest of capture-recapture studies but should not be analyzed using simplistic methods.
- Lessons from Petersen estimator area transferable to other experiments and models
- Use conditional MLE because it can deal with covariates in a unified fashion.
- Chapman correction factor only needed for small samples, but with small numbers of marks back, estimate will have poor precision.
- Confidence intervals can be found in many ways:
- \(\widehat{N} \pm 2 se\) in large samples
- Transform to \(log()\) scale, find ci, back transform in smallish samples
The key assumptions are:
- Population is closed
- If death only, then estimates \(\widehat{N}_1\)
- If births only, then estimates \(\widehat{N}_2\)
- If births and deaths, then estimates total animals available
- No tag loss
- Leads to positive bias in estimated population size
- Need to double tag some or all of animals with permanent mark or second tag of same or different type
- Need to adjust SE if only an estimate of tag loss is available.
- All tags seen and/or all tags reported
- Leads to positive bias in estimate population size
- Resample to look for lost tags; offer reward tags
- Need to adjust SE if only estimate of tag reporting is available.
- No marking effect on catchability
- Trap happiness leads to negative bias in population estimate
- Trap shyness leads to positive bias in population estimate
- Impossible to design study to adjust for problem as no control group possible
- Perhaps use different trapping methods
- No marking effect on survival (e.g. no acute tagging mortality)
- Leads to positive bias in population estimate
- Impossible to design study to adjust for problem as no control group possible
- Complete Mixing and/or homogeneity of catchability
- Pure heterogeneity leads to negative bias in population estimate
- Mixed heterogeneity can lead to positive or negative bias in population estimate
- Good study design to ensure that all of relevant population is sampled; gear should be non-selective
- Regular, or Geographical (SPAS) or temporal stratification (BTSPAS) may be needed.
You are likely to unsatisfied with geographical stratification because of the many parameters that must be estimated and with sparse data, the high degree of singularity in the recapture matrix.
It is essential to recapture sufficient number of marked animals.
- Rule of thumb is that \(rse \approx \frac{1}{\sqrt{marks~returned}}\)
- Precision can be improved by combining multiple Petersen estimates
- Possible to combine Petersen with other methods such as acoustic sampling; change in ratio; CPUE; etc (see me for details)
No amount of statistical wizardry can salvage a poorly designed study with insufficient marks back.
16 Miscellaneous notes
16.1 Speeding computation times
The computations in the examples in this monograph proceed quite quickly. However, there are times where the individual capture-history data structure may involve many thousands of individuals all with same capture-history.
Computation times can be considerably reduced by creating a condensed data set where the freq variable represents the number of animals with the same capture history. This speed up can be important when doing simulation studies.
data(data_NorthernPike)Consider the NorthernPike example. This has rows for the 7805 individual fish in the capture-history array. This can be condensed to a similar format at the Rodli example:
# create condensed dataset
data_NorthernPike.condensed <- plyr::ddply(data_NorthernPike,
c("cap_hist","Sex"),
plyr::summarize,
freq=length(Sex))
data_NorthernPike.condensed
## cap_hist Sex freq
## 1 01 F 524
## 2 01 M 459
## 3 10 F 3956
## 4 10 M 2709
## 5 11 F 89
## 6 11 M 68Both data forms give the same estimates (as expected) but the difference in computation times is:
# Fit the various models
t.condensed.start <- Sys.time()
nop.condensed <- Petersen::LP_fit(data_NorthernPike.condensed, p_model=~-1+..time)
t.condensed.end <- Sys.time()
t.full.start <- Sys.time()
nop.full <- Petersen::LP_fit(data_NorthernPike, p_model=~-1+..time)
t.full.end <- Sys.time()
cat("The two estimates \n")
## The two estimates
nop.condensed$summary
## p_model name_model cond.ll n.parms nobs method
## 1 ~-1 + ..time p: ~-1 + ..time -3702.341 2 7805 cond ll
nop.full $summary
## p_model name_model cond.ll n.parms nobs method
## 1 ~-1 + ..time p: ~-1 + ..time -3702.341 2 7805 cond ll
cat("Time to run the condensed data structure: ", t.condensed.end - t.condensed.start, "seconds \n")
## Time to run the condensed data structure: 0.0771389 seconds
cat("Time to run the full data structure: ", t.full.end - t.full.start, "seconds \n")
## Time to run the full data structure: 0.991904 seconds17 References
Akaike, H. (1973). Information Theory as an Extension of the Maximum Likelihood Principle. In Second International Symposium on Information Theory, edited by B. N. Petrov and F. Csaki, 267–281. Budapest: Akademiai Kiado.
Arbeider, M., Challenger, W., Dionne, K., Fisher, A., Noble, C., Parken, C., Ritchiel, L, and Robichaud, D. (2020) Estimating Aggregate Coho Salmon Terminal Run and Escapement to the Lower Fraser Management Unit. Report prepared for the Pacific Salmon Commission, dated 2020-02-21. Available at: https://www.psc.org/fund-project/feasibility-of-estimating-aggregate-coho-salmon-escapement-to-the-lower-fraser-management-unit/
Arnason, A. N., and K. H. Mills. (1981). Bias and Loss of Precision Due to Tag Loss in Jolly-Seber Estimates for Mark-Recapture Experiments. Canadian Journal of Fisheries and Aquatic Sciences 38, 1077–1095.
Arnason, A. N., C. W. Kirby, C. J. Schwarz, and J. R. Irvine. (1996). Computer analysis of data from stratified mark-recovery experiments for estimation of salmon escapements and other populations. Can. Tech. Rep. Fish. Aquat. Sci. 2106: vi+37 p.
Bailey, N. T. J. (1951). On estimating the size of mobile populations from capture-recapture data. Biometrika 38, 293–306.
Bailey, N. T. J. (1952). Improvements in the interpretation of recapture data. Journal of Animal Ecology 21, 120–127. https://doi.org/10.2307/1913
Beverton, R. J. H., and Holt, S. J. (1957). On the dynamics of exploited fish populations. Fish. Invest. Minist. Mar. Fish. Minist. Agric., Fish. Food. (G.B.), Ser. 11, 19, 533 p.
Bjorkstedt E. P. (2000). DARR (Darroch Analysis with Rank-Reduction): A method for analysis of stratified mark-recapture data from small populations, with application to estimating abundance of smolts from outmigrant trap data. Administrative Report SC-00-02, National Marine Fisheries Service. Available at: http://swfsc.noaa.gov/publications/FED/00116.pdf, Accessed 2009-07-28.
Bonner Simon, J. and Schwarz Carl, J. (2011). Smoothing Population Size Estimates for Time-Stratified Mark Recapture Experiments Using Bayesian P-Splines. Biometrics, 67, 1498–1507.
Bonner, S. J., & Holmberg, J. (2013). Mark-Recapture with Multiple, Non-Invasive Marks. Biometrics, 69, 766–-775. http://www.jstor.org/stable/24538143
Bonner, S. J. and Schwarz, C. J. (2023). BTSPAS: Bayesian Time Stratified Petersen Analysis System. R package version 2021.11.2.
Bruesewitz, R., and K. Reeves. (2005). Estimating Northern Pike Abundance at Mille Lacs Lake, Minnesota. Fisheries Research Proposal. Minnesota Department of Natural Resource., Unpublished Material.
Burnham, K. P., and Anderson, D. R. 2002. Model Selection and Multi-Model Inference: A Practical Information-Theoretic Approach. 2nd ed. New York: Springer.
Chapman, D. H. (1951). Some Properties of the Hypergeometric Distribution with Applications to Zoological Censuses. Univ Calif Public Stat 1, 131–60.
Chen, S. and Lloyd, C. (2000). A non-parametric approach to the analysis of two stage mark-recapture experiments. Biometrika 88, 649–663.
Cochran, W. G. (1977). Sampling Techniques, 3rd Edition. 3rd ed. New York: Wiley.
Cowen, Laura, and Schwarz, C. J. (2006). The Jolly-Seber Model with Tag Loss. Biometrics 62, 699–705. https://doi.org/10.1111/j.1541-0420.2006.00523.x.
Darroch, J. N. (1961). The two-sample capture-recapture census when tagging and sampling are stratified. Biometrika, 48, 241–260. https://www.jstor.org/stable/2332748
Goudie, I. B. J., and M. Goudie. (2007). Who Captures the Marks for the Petersen Estimator? Journal of the Royal Statistical Society. Series A (Statistics in Society), 170, 825–-839. http://www.jstor.org/stable/4623202
Gulland, J. A. (1963). On the Analysis of Double-Tagging Experiments. Special Publication ICNAF No. 3, 228–29.
Hamazaki, T. and DeCovich, N. (2014). Application of the Genetic Mark–Recapture Technique for Run Size Estimation of Yukon River Chinook Salmon. North American Journal of Fisheries Management, 34, 276–286. DOI: 10.1080/02755947.2013.869283
Hyun, S.-Y., Reynolds.J.H., and Galbreath, P.F. (2012). Accounting for Tag Loss and Its Uncertainty in a Mark–Recapture Study with a Mixture of Single and Double Tags. Transactions of the American Fisheries Society, 141, 11–25. http://dx.doi.org/10.1080/00028487.2011.639263
Huggins, R. M. 1989. On the Statistical Analysis of Capture Experiments. Biometrika 76: 133–40.
Jackson, C. H. N. (1933). On the True Density of Tsetse Flies. Journal of Animal Ecology 2, 204–209.
Junge, C. O. (1963). A Quantitative Evaluation of the Bias in Population Estimates Based on Selective Samples. I.C.N.A.F. Special Publication No. 4, 26–28.
Laake J (2013). RMark: An R Interface for Analysis of Capture-Recapture Data with MARK. AFSC Processed Rep. 2013-01, Alaska Fish. Sci. Cent., NOAA, Natl. Mar. Fish. Serv., Seattle, WA. https://apps-afsc.fisheries.noaa.gov/Publications/ProcRpt/PR2013-01.pdf.
Laplace, P. S. (1786). Sur Les Naissances, Les Mariages et Les Morts. Histoire de l’Academie Royale Des Sciences, Annee 1783, no. 693.
Lincoln, F. C. (1930). Calculating Waterfowl Abundance on the Basis of Banding Returns. United States Department of Agriculture Circular No. 118, 1–4.
Link, W. A. (2003). Nonidentifiability of Population Size from Capture-Recapture Data with Heterogeneous Detection Probabilities. Biometrics 59, 1123–1130.
Link, W. A., and R. J. Barker. (2005). Modeling Association among Demographic Parameters in Analysis of Open Population Capture-Recapture Data. Biometrics 61, 46–54.
McClintock, B.T., Conn, P.B., Alonso, R.S. and Crooks, K.R. (2013), Integrated modeling of bilateral photo-identification data in mark–recapture analyses. Ecology, 94, 1464–1471. https://doi.org/10.1890/12-1613.1
McClintock, B. T. (2015) multimark: an R package for analysis of capture-recapture data consisting of multiple “noninvasive” marks. Ecology and Evolution 5, 4920–4931.
Mantyniemi, S. and Romakkaniemi, A. (2002). Bayesian mark-recapture estimation with an application to a salmonid smolt population. Canadian Journal of Fisheries and Aquatic Science 59, 1748–1758.
McClintock BT, White GC, Antolin MF, Tripp DW (2009) Estimating abundance using mark-resight when sampling is with replacement or the number of marked individuals is unknown. Biometrics 65, 237–-246
McClintock, B.T., White, G.C. (2012) From NOREMARK to MARK: software for estimating demographic parameters using mark–resight methodology. J Ornithol 152 (Suppl 2), 641–-650. https://doi.org/10.1007/s10336-010-0524-x
McDonald, T. L., S. C. Amstrup, and B. F. J. Manly. (2003). Tag Loss Can Bias Jolly-Seber Capture-Recapture Estimates. Wildlife Society Bulletin 31, 814–822.
Petersen, C. G. J. (1896). The Yearly Immigration of Young Plaice into the Limfjord from the German Sea, Etc. Report Danish Biological Station 6, 1–48.
Plante, N., L.-P Rivest, and G. Tremblay. (1988). Stratified Capture-Recapture Estimation of the Size of a Closed Population. Biometrics 54, 47–60. https://www.jstor.org/stable/2533994
Premarathna, W.A.L., Schwarz, C.J., Jones, T.S. (2018) Partial stratification in two-sample capture–recapture experiments. Environmetrics, 29:e2498. https://doi.org/10.1002/env.2498
Rawding, D.J., Sharpe, C.S. and Blankenship, S.M. (2014), Genetic-Based Estimates of Adult Chinook Salmon Spawner Abundance from Carcass Surveys and Juvenile Out-Migrant Traps. Transactions of the American Fisheries Society, 143, 55–67. https://doi.org/10.1080/00028487.2013.829122
Rajwani, K., and Schwarz, C.J. (1997). Adjusting for Missing Tags in Salmon Escapement Surveys. Canadian Journal of Fisheries and Aquatic Sciences, 54, 800–808.
Ricker, W. E. (1975). Computation and Interpretation of Biological Statistics of Fish Populations. Bull Fish Res Board Can 191.
Robson, D. S., and H. A. Regier. (1964). Sample Size in Petersen Mark-Recapture Experiments. Transactions of the American Fish Society 93, 215–26. https://doi.org/10.1577/1548-8659(1964)93[215:SSIPME]2.0.CO;2
Rosenbaum, S. W., May, S. A., Shedd, K. R., Cunningham, C. J., Peterson, R. L., Elliot, B. W., & McPhee, M. V. (2024). Reliability of trans-generational genetic mark–recapture (tGMR) for enumerating Pacific salmon. Evolutionary Applications, 17, e13647. https://doi.org/10.1111/eva.13647
Schwarz, C. J. (2023). SPAS: Stratified-Petersen Analysis System. R package version 2023.3.31.
Schwarz, C. J., Andrews, M., & Link, M. R. (1999). The Stratified Petersen Estimator with a Known Number of Unread Tags. Biometrics, 55, 1014–-1021.
Schwarz, C. J. and Dempson, J. B. (1994). Mark-recapture estimation of a salmon smolt population. Biometrics, 50, 98–108.
Schwarz, C. J. and Taylor, C. G. (1998). The use of the stratified-Petersen estimator in fisheries management: estimating the number of pink salmon (Oncorhynchus gorbuscha) that spawn in the Fraser River. Canadian Journal of Fisheries and Aquatic Sciences 55, 281–297. https://doi.org/10.1139/f97-238
Seber, G. A. F. (1982). The Estimation of Animal Abundance and Related Parameters. 2nd ed. London: Griffin.
Seber, G. A. F., and R. Felton. (1981). Tag Loss and the Petersen Mark-Recapture Experiment. Biometrika 68, 211–19.
Seber, G.A. F. and M. R. Schofield (2023), Estimating Presence and Abundance of Closed Populations, Statistics for Biology and Health, Springer, New York. https://doi.org/10.1007/978-3-031-39834-6_1
Sprott, D. A. (1981). Maximum Likelihood Applied to a Capture-Recapture Model. Biometrics 37, 371–375.
Wang, J., & Santure, A. W. (2009). Parentage and Sibship in- ference from multilocus genotype data under polygamy. Genetics, 181(4), 1579–-1594. https://doi.org/10.1534/genetics.108.100214
Weatherall, J. A. (1982). Analysis of Double Tagging Experiments. Fishery Bulletin 80, 687–701.
White, G.C. and K. P. Burnham. 1999.
Program MARK: Survival estimation from populations of marked animals. Bird Study 46 Supplement, 120–138.
Williams, B. K., J. D. Nichols, and M. J. Conroy. (2002). Analysis and Management of Animal Populations. New York: Academic Press.
Yee, T.W., Stoklosa, J., and Huggins, R.J. (2015). The VGAM Package for Capture-Recapture Data Using the Conditional Likelihood. Journal of Statistical Software, 65, 1–33. DOI: 10.18637/jss.v065.i05. URL https://www.jstatsoft.org/article/view/v065i05/.
papers by Rivest on the proper constant to add to the Petersen to make unbiased. See Canadian Journal of Statistics.
Morrison book
Paper on bayesian stratified petersen
paper on petersen with recognition errors Stevick, P., Palsbøll, P., Smith, T., Bravington, M., and Hammond, P.. (2011). Errors in identification using natural markings: rates, sources, and effects on capture-recapture estimates of abundance. Canadian Journal of Fisheries and Aquatic Sciences. 58. 1861-1870. DOI: 10.1139/f01-131.
18 Appendix A - The multinomial models for the Petersen study
As indicated earlier, the predominant paradigm currently used in capture-recapture studies is the multinomial model based on the observed capture histories. This formulation assume that neither \(n_1\) nor \(n_2\) nor \(m_2\) are fixed quantities, but are all random variables.
There are two (asymptotically) equivalent multinomial formulations. The first is the complete multinomial where the abundance enters directly into the likelihood formulation. In this formulation an implicit assumption is that capture probabilities are known for animals never seen, i.e., are equal to the capture probabilities for animals that are seen in the study. In some cases, catchability is heterogeneous among fish, and the catchability may be related to a fixed covariates, such as fish length. Unfortunately, the fish length for fish never captured is unknown and so the capture probability for fish with history (00) cannot be modeled. Huggins (1989) showed that a conditional (upon fish been seen) multinomial model could be used in these circumstances. This chapter will develop these two formulations.
18.1 Complete multinomial model
The statistics for this formulation are the number with each capture history, \(n_{10}, n_{01}, n_{11}\). Assuming no losses on capture, the probabilities of these histories and history (00) are
\[P\left( {\left\{ {10} \right\}} \right) = p_1 \left( {1 - p_2 } \right) \] \[P\left( {\left\{ {01} \right\}} \right) = \left( {1 - p_1 } \right) p_2\] \[P\left( {\left\{ {11} \right\}} \right) = p_1 p_2\] \[P\left( {\left\{ {00} \right\}} \right) = \left( {1 - p_1 } \right)\left( {1 - p_2 } \right)\]
The likelihood function is a multinomial distribution among these observed capture histories and probabilities: \[L= \binom{N}{n_{00},n_{01},n_{10},n_{11}} \times \left[ {p_1 \left( {1 - p_2 } \right)} \right]^{n_{10} } \left[ {\left( {1 - p_1 } \right)p_2 } \right]^{n_{01} } \left[ {p_1 p_2 } \right]^{n_{11} } \left[ {\left( {1 - p_1 } \right)\left( {1 - p_2 } \right)} \right]^{N - n_{10} - n_{01} - n_{11} }\] The key difference between ordinary multinomial distributions and this likelihood is the presence of the unknown parameter \(N\) in the combinatorial term.
The estimators are found by maximizing the \(log(L)\) by taking first-derivatives, setting these to zero, and solving. The estimating equations for \(p_1\) and \(p_2\) are found to be:
- \(\left( {n_{11} + n_{10} } \right) = Np_1\)
- \(\left( {n_{11} + n_{01} } \right) = Np_2\)
Because the parameter \(N\) appears in factorial term, rather than taking first derivatives, the first difference is found, i.e., \(log(L(N))-log(L(N-1))=0\) which leads to the estimating equation: \[\left( {\frac{{N\left( {1 - p_1 } \right)\left( {1 - p_2 } \right)}}{{N - n_{10} - n_{01} - n_{11} }}} \right) = 0\] Not surprisingly, this leads to the same estimators as seen earlier, namely: \[\hat N = \frac{{\left( {n_{11} + n_{10} } \right)\left( {n_{11} + n_{01} } \right)}}{{n_{11} }} = \frac{{n_1 n_2 }}{{m_2 }} \] \[\hat p_1 = \frac{{\left( {n_{11} + n_{10} } \right)}}{{\hat N}} = \frac{{n_{11} }}{{\left( {n_{11} + n_{01} } \right)}} = \frac{{m_2 }}{{n_2 }}\] \[\hat p_2 = \frac{{\left( {n_{11} + n_{01} } \right)}}{{\hat N}} = \frac{{n_{11} }}{{\left( {n_{11} + n_{10} } \right)}} = \frac{{m_2 }}{{n_1 }}\]
Because it is possible for no marks to be recaptured (\(m_2=0\)), the same adjustments to the MLE can be made as found in the other estimators presented in Table 1.
The information matrix (the negative of the expected value of the second derivative matrix) is found by differentiating the first derivative or difference equations and replacing the observed statistics (the number of fish with each capture history) with its expected value. If the parameters are ordered by \(N\), \(p_1\), and \(p_2\), the information matrix is: \[\left[ {\begin{array}{*{20}c} {\frac{{1 - \left( {1 - p_1 } \right)\left( {1 - p_2 } \right)}}{{N\left( {1 - p_1 } \right)\left( {1 - p_2 } \right)}}} & {\frac{1}{{(1 - p_1 )}}} & {\frac{1}{{(1 - p_2 )}}} \\ {\frac{1}{{(1 - p_1 )}}} & {\frac{N}{{p_1 (1 - p_1 )}}} & 0 \\ {\frac{1}{{(1 - p_2 )}}} & 0 & {\frac{N}{{p_2 (1 - p_2 )}}} \\ \end{array}} \right]\]
The inverse of this matrix provides the variance-covariance matrix of the estimators: \[\left[ {\begin{array}{*{20}c} {\frac{{N\left( {1 - p_1 } \right)\left( {1 - p_2 } \right)}}{{p_1 p_2 }}} & {\frac{{ - \left( {1 - p_1 } \right)\left( {1 - p_2 } \right)}}{{p_2 }}} & {\frac{{ - \left( {1 - p_1 } \right)\left( {1 - p_2 } \right)}}{{p_1 }}} \\ {\frac{{ - \left( {1 - p_1 } \right)\left( {1 - p_2 } \right)}}{{p_2 }}} & {\frac{{p_1 (1 - p_1 )}}{{Np_2 }}} & {\frac{{\left( {1 - p_1 } \right)\left( {1 - p_2 } \right)}}{N}} \\ {\frac{{ - \left( {1 - p_1 } \right)\left( {1 - p_2 } \right)}}{{p_1 }}} & {\frac{{\left( {1 - p_1 } \right)\left( {1 - p_2 } \right)}}{N}} & {\frac{{p_2 (1 - p_2 )}}{{Np_1 }}} \\ \end{array}} \right]\]
The precision of the estimated abundance is
\[se\left( {\hat N} \right) = \sqrt {N\frac{{\left( {1 - p_1 } \right)}}{{p_1 }}
\frac{{\left( {1 - p_2 } \right)}}{{p_2 }}}\] If the capture probabilities are small, then \(\frac{1-p_i}{p_i}\) is large, and the precision is poor. An estimated \(SE\) is found by replacing the unknown parameters by their estimators to give: \[\widehat{se}\left( {\hat N} \right) = \sqrt {\frac{{n_1 n_2 }}{{m_2 }}\frac{{\left( {n_2 - m_2 } \right)}}{{m_2
}}\frac{{\left( {n_1 - m_2 } \right)}}{{m_2 }}}\] which again is very similar to the results presented in Table 1. Again, similar sorts of adjustments can be made (adding 1 to various terms) to avoid problems with zero counts.
18.2 Conditional multinomial model
The Huggins (1989) conditional multinomial model is most useful when the capture probabilities are modeled as functions of individual covariates and is not needed for the basic Petersen estimator. However, this development that follows will show how the basic conditional model is developed.
Now only animals that are seen at least once are used in the likelihood. The statistics for this formulation are the number with each capture history, \(n_{10}, n_{01}, n_{11}\). Assuming no losses on capture, the conditional probability of each of these histories is found by normalizing the probabilities found in the previous section, by the total probability of been seen in the study.
\[P\left( {\left\{ {10} \right\}} \right) = \frac{p_1 \left( {1 - p_2 } \right)}{1-(1-p_1)(1-p_2)}\] \[P\left( {\left\{ {01} \right\}} \right) = \frac{\left( {1 - p_1 } \right)p_2}{1-(1-p_1)(1-p_2)}\] \[P\left( {\left\{ {11} \right\}} \right) = \frac{p_1 p_2}{1-(1-p_1)(1-p_2)}\]
Notice that the probability of history (00) is not needed.
The conditional likelihood function is a multinomial distribution among these observed capture histories and probabilities: \[L= \binom{n_{obs}}{n_{01},n_{10},n_{11}} \times \left[ {\frac{{p_1 \left( {1 - p_2 } \right)}}{1-(1-p_1)(1-p_2)}} \right]^{n_{10}} \left[ {\frac{{\left( {1 - p_1 } \right)p_2 }}{1-(1-p_1)(1-p_2)}} \right]^{n_{01} } \left[ {\frac{{p_1 p_2 }} {1-(1-p_1)(1-p_2)}} \right]^{n_{11} } \]
where \(n_{obs}=n_{01} + n_{10} + n_{11}\). Now no unknown parameter appears in the combinatorial term and the population abundance is not modeled..
The estimators are found by maximizing the \(log(L)\) by taking first-derivatives, setting these to zero, and solving. The conditional maximum likelihood estimates for \(p_1\) and \(p_2\) are found to be the same as in the complete multinomial case:
- \(\widehat{p}_1 = \frac{n_{11} }{\left( {n_{11} + n_{01} } \right) }\)
- \(\widehat{p}_2 = \frac{n_{11} }{\left( {n_{11} + n_{10} } \right) }\)
The information matrix (the negative of the expected value of the second derivative matrix) is found by differentiating the first derivative or difference equations and replacing the observed statistics (the number of fish with each capture history) with its expected value. The inverse of this gives the covariance matrix of the estimates. If the parameters are ordered by \(p_1\), and \(p_2\), the covariance matrix is:
\[\begin{equation} {Var}_{cond}\left[ {\begin{array}{c} {\hat p_1^{cond} } \\ {\hat p_1^{cond} } \\ \end{array}} \right]= \left[ { \begin{array}{cc} \frac{p_1 \left( {1 - p_1 } \right) }{n_{obs}p_2/{\left( {1 - \left({1-p_1}\right)\left({1-p_2}\right)}\right)}}& \frac{\left( {1 - p_1 } \right) \left( {1 - p_2 } \right)}{n_{obs}/{\left( {1 - \left({1-p_1}\right)\left({1-p_2}\right)}\right)}}\\ \frac{\left( {1 - p_1 } \right) \left( {1 - p_2 } \right)}{n_{obs}/{\left( {1 - \left({1-p_1}\right)\left({1-p_2}\right)}\right)}} & \frac{p_2 \left( {1 - p_2 } \right) }{n_{obs}p_1/{\left( {1 - \left({1-p_1}\right)\left({1-p_2}\right)}\right)}}\\ \end{array} }\right] \end{equation}\]
The variances of the capture probabilities are very similar to those in the complete multinomial models being of the form \(\frac{p_i(1-p_i)}{\textit{Expected number of fish captured at the other occasion}}\). There is asymptotically no loss in information about the capture probabilities by using the conditional model – again this is not surprising as the unknown number of fish never seen can’t provide information about the capture probabilities.
The estimated variances are found by substituting in the estimated capture probabilities and reduce to a surprisingly simple form: \[\widehat{{\mathop{\textrm{var}}} }_{cond} \left[ {\begin{array}{*{20}c} {\hat p_1^{cond} } \\ {\hat p_1^{cond} } \\ \end{array}} \right] = \left[ {\begin{array}{*{20}c} {\frac{{n_{11} n_{01} }}{{\left( {n_{01} + n_{11} } \right)^3 }}} & {\frac{{n_{11} n_{10} n_{01} }}{{\left( {n_{01} + n_{11} } \right)^2 \left( {n_{10} + n_{11} } \right)^2 }}} \\ {\frac{{n_{11} n_{10} n_{01} }}{{\left( {n_{01} + n_{11} } \right)^2 \left( {n_{10} + n_{11} } \right)^2 }}} & {\frac{{n_{11} n_{10} }}{{\left( {n_{10} + n_{11} } \right)^3 }}} \\ \end{array}} \right]\]
Huggins (1989) showed that an estimator for the abundance can be obtained as: \[\widehat{N}_{cond} = \sum\limits_{\textrm{{obs~animals}}}^{} {\frac{1}{{\hat p}_a^*}}\] where \(\hat{p}^*_a\) is the probability of seeing animal \(a\) in the study. In this simple Petersen study all animals have the same probability of being seen in the study, namely \(1-(1-p_1)(1-p_2)\) and the estimated abundance reduces to: \[\widehat{N}_{cond} = \frac{{n_{obs} }}{{1 - \left( {1 - \hat p_1 } \right)\left( {1 - \hat p_2 } \right)}} = \frac{{\left( {n_{10} + n_{11} } \right)\left( {n_{01} + n_{11} } \right)}}{{n_{11} }} = \frac{{n_1 n_2 }}{{m_2 }}\] which is the familiar Petersen estimator.
Huggins (1989) also gave an expression for the estimated variance of \(\widehat{N}\): \[ \widehat{\textrm{var} }\left( {\widehat{N}_{cond} } \right) = \sum\limits_{{\textrm{obs animals}}}^{} {\frac{{1 - \hat p_a^* }}{{\left( {\hat p_a^* } \right)^2 }}} + \widehat{D}^T \hat I^{ - 1} \widehat{D} \] where \(\widehat{D}\) is the partial derivative of the estimator \(\widehat{N}\) with respect to the catchabilities \(p_1\) and \(p_2\), and \(\widehat{I}^{-1}\) is the estimated covariance matrix of the estimated catchabilities.
Long and tedious algebra reduces to the familiar form: \[ \widehat{\textrm{var}}\left( {\widehat{N}_{cond} } \right) = \frac{{n_{01} n_{10} \left( {n_{01} + n_{11} } \right)\left( {n_{10} + n_{11} } \right)}}{{n_{_{11} }^3 }} = \frac{{n_1 n_2 (n_1 - m_2 )(n_2 - m_2 )}}{{m_2^3 }} \]
The conditional multinomial estimator is fully efficient – a conclusion echoed by Link and Barker (2005) who showed that there is no loss in information in using a conditional multinomial model to estimate abundance in the more general open-population capture-recapture setting.
For these reasons, we will ONLY use the conditional multinomial model in the Petersen package following the work of Yee et al (2015).
19 Appendix B - Using the VGAM package
Yee et al. (2015) developed the VGAM package which includes functions for fitting closed-population capture-recapture models, of which the Petersen-type studies are special cases. We will illustrate the use of this package with the Rödli Tarn data.
19.1 Data structure
The data structure to use the VGAM functions is slightly different from the data structure used by the Petersen package.
A data.frame is constructed with
- Two variables (traditionally called t1 and t2) for the capture history which must be numeric columns with 0 representing not captured and 1 representing captured. The Petersen package includes the split_cap_hist() function that can split the capture history represented by a single string.
- Each animal must represented by its own record. Hence, grouped capture histories with a freq variable must be expanded to individual records.
See details in the examples below.
Yee et al. (2015) provides supplemental materials with code examples from this the following were derived.
19.2 Example Rodli Tarn
This was analyzed using the Petersen package in Section 3.5.1.
In this example, we first demonstrate how to split the capture histories and expand capture histories to individual records required for the VGAM functions.
library(VGAM)
data(data_rodli)
# split the capture histories
rodli.vgam <- cbind(data_rodli,
Petersen::split_cap_hist(data_rodli$cap_hist,
make.numeric=TRUE))
# need to expand capture history by frequency
rodli.vgam.expand <- plyr::adply(rodli.vgam, 1, function(x){
x[ rep(1, x$freq),]
})
head(rodli.vgam.expand)
## cap_hist freq t1 t2
## 1 11 57 1 1
## 2 11 57 1 1
## 3 11 57 1 1
## 4 11 57 1 1
## 5 11 57 1 1
## 6 11 57 1 1Then the traditional Petersen estimator is the Mt model (in the parlance of the closed-population capture-recapture models).
rodli.vgam.m.t <- vglm(cbind(t1,t2) ~ 1,
posbernoulli.t, data = rodli.vgam.expand)
summary(rodli.vgam.m.t)
##
## Call:
## vglm(formula = cbind(t1, t2) ~ 1, family = posbernoulli.t, data = rodli.vgam.expand)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept):1 -0.74444 0.16086 -4.628 3.7e-06 ***
## (Intercept):2 0.09181 0.19177 0.479 0.632
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Names of linear predictors: logitlink(E[t1]), logitlink(E[t2])
##
## Log-likelihood: -233.9047 on 456 degrees of freedom
##
## Number of Fisher scoring iterations: 4
##
## No Hauck-Donner effect found in any of the estimates
##
##
## Estimate of N: 338.474
##
## Std. Error of N: 25.496
##
## Approximate 95 percent confidence interval for N:
## 288.5 388.4519.3 Example Rodli Tarn - Chapman correction
This was analyzed using the Petersen package in Section 3.5.2.
library(VGAM)
data(data_rodli)
# add extra animal that is tagged and recaptured
rodli.chapman <- plyr::rbind.fill(data_rodli,
data.frame(cap_hist="11", freq=1, comment="Added for Chapman"))
# split the capture history
rodli.vgam.chapman <- cbind(rodli.chapman,
Petersen::split_cap_hist(rodli.chapman$cap_hist,
make.numeric=TRUE))
# need to expand capture history by frequency
rodli.vgam.chapman.expand <- plyr::adply(rodli.vgam.chapman, 1, function(x){
x[ rep(1, x$freq),]
})
head(rodli.vgam.chapman.expand)
## cap_hist freq comment t1 t2
## 1 11 57 <NA> 1 1
## 2 11 57 <NA> 1 1
## 3 11 57 <NA> 1 1
## 4 11 57 <NA> 1 1
## 5 11 57 <NA> 1 1
## 6 11 57 <NA> 1 1
# fit the Mt model with the Chapman correction
rodli.vgam.M.t.chapman <- vglm(cbind(t1,t2) ~ 1,
posbernoulli.t, data = rodli.vgam.chapman.expand)
summary(rodli.vgam.M.t.chapman)
##
## Call:
## vglm(formula = cbind(t1, t2) ~ 1, family = posbernoulli.t, data = rodli.vgam.chapman.expand)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept):1 -0.7270 0.1599 -4.546 5.46e-06 ***
## (Intercept):2 0.1092 0.1910 0.572 0.567
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Names of linear predictors: logitlink(E[t1]), logitlink(E[t2])
##
## Log-likelihood: -235.2889 on 458 degrees of freedom
##
## Number of Fisher scoring iterations: 4
##
## No Hauck-Donner effect found in any of the estimates
##
##
## Estimate of N: 337.586
##
## Std. Error of N: 25.024
##
## Approximate 95 percent confidence interval for N:
## 288.54 386.6319.4 Example - Rodli Tarn - Equal capture probabilities
This was analyzed by the Petersen package in Section 3.5.3.
library(VGAM)
data(data_rodli)
# split the capture history
rodli.vgam <- cbind(data_rodli,
Petersen::split_cap_hist(data_rodli$cap_hist,
make.numeric=TRUE))
# need to expand capture history by frequency
rodli.vgam.expand <- plyr::adply(rodli.vgam, 1, function(x){
x[ rep(1, x$freq),]
})
# fit the model
rodli.vgam.m.0 <- vglm(cbind(t1,t2) ~ 1,
posbernoulli.t(parallel = TRUE ~ 1), data = rodli.vgam.expand)
summary(rodli.vgam.m.0)
##
## Call:
## vglm(formula = cbind(t1, t2) ~ 1, family = posbernoulli.t(parallel = TRUE ~
## 1), data = rodli.vgam.expand)
##
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) -0.4113 0.1528 -2.691 0.00712 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Names of linear predictors: logitlink(E[t1]), logitlink(E[t2])
##
## Log-likelihood: -247.7207 on 457 degrees of freedom
##
## Number of Fisher scoring iterations: 4
##
## No Hauck-Donner effect found in any of the estimates
##
##
## Estimate of N: 358.754
##
## Std. Error of N: 28.577
##
## Approximate 95 percent confidence interval for N:
## 302.74 414.76
# aic table
library(AICcmodavg)
AICcmodavg::aictab(list(rodli.vgam.m.0,
rodli.vgam.m.t))
##
## Model selection based on AICc:
##
## K AICc Delta_AICc AICcWt Cum.Wt LL
## Mod2 2 471.86 0.0 1 1 -233.90
## Mod1 1 497.46 25.6 0 1 -247.7219.5 Example - Northern Pike - Stratification by Sex
This was analyzed by the Petersen package in Section 6.2.
library(VGAM)
data(data_NorthernPike)
# split the capture history
NorthernPike.vgam <- cbind(data_NorthernPike,
Petersen::split_cap_hist(data_NorthernPike$cap_hist,
make.numeric=TRUE))
nop.vgam.time <- vglm(cbind(t1,t2) ~ 1,
posbernoulli.t,
data = NorthernPike.vgam)
nop.vgam.sex.time <- vglm(cbind(t1,t2) ~ Sex,
posbernoulli.t,
data = NorthernPike.vgam)
nop.vgam.sex.p.time <- vglm(cbind(t1,t2) ~ Sex,
posbernoulli.t(parallel = TRUE ~ Sex),
data = NorthernPike.vgam)
# aic table
library(AICcmodavg)
AICcmodavg::aictab(list(nop.vgam.time,
nop.vgam.sex.time,
nop.vgam.sex.p.time))
##
## Model selection based on AICc:
##
## K AICc Delta_AICc AICcWt Cum.Wt LL
## Mod1 2 7408.68 0.00 0.71 0.71 -3702.34
## Mod2 3 7410.46 1.78 0.29 1.00 -3702.23
## Mod3 2 12143.55 4734.86 0.00 1.00 -6069.77It is not possible to fit a model where the capture probabilities are equal at the first or second sampling event using the VGAM package.
19.6 Example - Northern Pike - Stratification by Length Class
library(VGAM)
data(data_NorthernPike)
# split the capture history
NorthernPike.vgam <- cbind(data_NorthernPike,
Petersen::split_cap_hist(data_NorthernPike$cap_hist,
make.numeric=TRUE))
# create the length classes
NorthernPike.vgam$length.class <- car::recode(NorthernPike.vgam$length,
" lo:20='00-20';
20:25='20-25';
25:30='25-30';
30:35='30-35';
35:hi='35+' ")
nop.vgam.time <- vglm(cbind(t1,t2) ~ 1,
posbernoulli.t,
data = NorthernPike.vgam)
nop.vgam.length.class.time <- vglm(cbind(t1,t2) ~ length.class,
posbernoulli.t,
data = NorthernPike.vgam)
nop.vgam.length.class.p.time <- vglm(cbind(t1,t2) ~ length.class,
posbernoulli.t(parallel = TRUE ~ length.class),
data = NorthernPike.vgam)
# aic table
library(AICcmodavg)
AICcmodavg::aictab(list(nop.vgam.time,
nop.vgam.length.class.time,
nop.vgam.length.class.p.time))
##
## Model selection based on AICc:
##
## K AICc Delta_AICc AICcWt Cum.Wt LL
## Mod2 6 7368.04 0.00 1 1 -3678.01
## Mod1 2 7408.68 40.64 0 1 -3702.34
## Mod3 5 12101.12 4733.09 0 1 -6045.56It is not possible to fit a model where the capture probabilities are equal at the first or second sampling event using the VGAM package.
20 Appendix C. Using RMark/MARK
MARK (White and Burnham, 1999) is a Windows-based program for the analysis of capture-recapture experiments that can analyze many different types of studies RMark (Laake, 2013) is an R front-end that allows for a formula-type specification for models (rather than the graphical interface used in MARK), but then calls MARK for actual computation.s
In this section, we will demonstrate how to use RMark/MARK for the analysis of basic capture-recapture experiments.
20.1 Data structure
The data structure to use the RMark/MARK functions is similar to the data structure used by the Petersen package.
A data.frame is constructed with
- variable ch representing the capture history (e.g., 01, 10, 11)
- a variable freq representing the number of animals with that history
- other variables indicating groups and covariates.
See details in the examples below.
20.2 Example Rodli Tarn
This was analyzed using the Petersen package in Section 3.5.1.
We first get the Rodli data and then change the capture history vector variable name:
library(RMark)
data(data_rodli)
data_rodli.mark <- plyr::rename(data_rodli, c("cap_hist"="ch"))
data_rodli.mark
## ch freq
## 1 11 57
## 2 10 52
## 3 01 120We will used the Huggins-conditional closed-population likelihood models.
# We will be fitting some closed population models the "Closed" models, so we need to know
# the parameters of the model
setup.parameters("Huggins", check=TRUE) # returns a vector of parameter names (case sensitive)
## [1] "p" "c"
# Notice that there is NO parameter for the population size in the Huggins model
rodli.rmark.mt <- mark( data_rodli.mark, invisible=TRUE,
model="Huggins",
model.name="model ~..time",
model.parameters=list(p=list(formula=~time, share=TRUE))
)
##
## Output summary for Huggins model
## Name : model ~..time
##
## Npar : 2
## -2lnL: 467.8095
## AICc : 471.8358
##
## Beta
## estimate se lcl ucl
## p:(Intercept) -0.7444405 0.1608639 -1.0597337 -0.4291472
## p:time2 0.8362480 0.1660244 0.5108402 1.1616559
##
##
## Real Parameter p
## 1 2
## 0.3220339 0.5229358
##
##
## Real Parameter c
## 2
## 0.5229358This gives much output, but we extract the relevant parts:
summary(rodli.rmark.mt, se=TRUE)
## Output summary for Huggins model
## Name : model ~..time
##
## Npar : 2
## -2lnL: 467.8095
## AICc : 471.8358
##
## Beta
## estimate se lcl ucl
## p:(Intercept) -0.7444405 0.1608639 -1.0597337 -0.4291472
## p:time2 0.8362480 0.1660244 0.5108402 1.1616559
##
##
## Real Parameter p
## all.diff.index par.index estimate se lcl ucl fixed
## p g1 t1 1 1 0.3220339 0.0351211 0.2573604 0.3943300
## p g1 t2 2 2 0.5229358 0.0478409 0.4294597 0.6148324
##
##
## Real Parameter c
## all.diff.index par.index estimate se lcl ucl fixed
## c g1 t2 3 2 0.5229358 0.0478409 0.4294597 0.6148324
rodli.rmark.mt$results$real
## estimate se lcl ucl fixed note
## p g1 t1 0.3220339 0.0351211 0.2573604 0.3943300
## p g1 t2 0.5229358 0.0478409 0.4294597 0.6148324As before, the estimate of the population size is obtained using a Horvitz-Thompson-like estimator and is not part of the likelihood. These are known as derived parameters in RMark/MARK:
rodli.rmark.mt$results$derived
## $`N Population Size`
## estimate se lcl ucl
## 1 338.4737 25.49646 298.7707 400.769620.3 Example Rodli Tarn - Chapman correction
This was analyzed using the Petersen package in Section 3.5.2.
library(RMark)
data(data_rodli)
data_rodli.mark <- plyr::rename(data_rodli, c("cap_hist"="ch"))
# add extra animal that is tagged and recaptured
data_rodli.chapman.mark <- plyr::rbind.fill(data_rodli.mark,
data.frame(ch="11", freq=1, comment="Added for Chapman"))
# fit the Mt model with the Chapman correction
rodli.rmark.mt.chapman <- mark( data_rodli.chapman.mark, invisible=TRUE,
model="Huggins",
model.name="model ~..time",
model.parameters=list(p=list(formula=~time, share=TRUE))
)
##
## Output summary for Huggins model
## Name : model ~..time
##
## Npar : 2
## -2lnL: 470.5777
## AICc : 474.604
##
## Beta
## estimate se lcl ucl
## p:(Intercept) -0.7270487 0.1599210 -1.0404938 -0.4136037
## p:time2 0.8362480 0.1660244 0.5108402 1.1616559
##
##
## Real Parameter p
## 1 2
## 0.3258427 0.5272727
##
##
## Real Parameter c
## 2
## 0.5272727
summary(rodli.rmark.mt.chapman, se=TRUE)
## Output summary for Huggins model
## Name : model ~..time
##
## Npar : 2
## -2lnL: 470.5777
## AICc : 474.604
##
## Beta
## estimate se lcl ucl
## p:(Intercept) -0.7270487 0.1599210 -1.0404938 -0.4136037
## p:time2 0.8362480 0.1660244 0.5108402 1.1616559
##
##
## Real Parameter p
## all.diff.index par.index estimate se lcl ucl fixed
## p g1 t1 1 1 0.3258427 0.0351297 0.2610547 0.3980483
## p g1 t2 2 2 0.5272727 0.0476022 0.4341067 0.6185773
##
##
## Real Parameter c
## all.diff.index par.index estimate se lcl ucl fixed
## c g1 t2 3 2 0.5272727 0.0476022 0.4341067 0.6185773
rodli.rmark.mt.chapman$results$real
## estimate se lcl ucl fixed note
## p g1 t1 0.3258427 0.0351297 0.2610547 0.3980483
## p g1 t2 0.5272727 0.0476022 0.4341067 0.6185773
rodli.rmark.mt.chapman$results$derived
## $`N Population Size`
## estimate se lcl ucl
## 1 337.5862 25.02399 298.6072 398.7109We need to remove the Chapman model because the data is different when we compare model using AIC (later)”
rm(rodli.rmark.mt.chapman)
cleanup(ask=FALSE)20.4 Example - Rodli Tarn - Equal capture probabilities
This was analyzed by the Petersen package in Section 3.5.3.
rodli.rmark.m0 <- mark( data_rodli.mark, invisible=TRUE,
model="Huggins",
model.name="model ~1",
model.parameters=list(p=list(formula=~1, share=TRUE))
)
##
## Output summary for Huggins model
## Name : model ~1
##
## Npar : 1
## -2lnL: 495.4414
## AICc : 497.4501
##
## Beta
## estimate se lcl ucl
## p:(Intercept) -0.411296 0.1528326 -0.710848 -0.111744
##
##
## Real Parameter p
## 1 2
## 0.3986014 0.3986014
##
##
## Real Parameter c
## 2
## 0.3986014We now can do the usual AIC model averaging on the two models
# Collect results and get the AIC tables
rodli.results <- collect.models( type="Huggins")
rodli.results
## model npar AICc DeltaAICc weight Deviance
## 2 model ~..time 2 471.8358 0.00000 9.999973e-01 2037.917
## 1 model ~1 1 497.4501 25.61429 2.741112e-06 2065.54920.5 Example - Northern Pike - Stratification by Sex
This was analyzed by the Petersen package in Section 6.2.
We create the proper data structures:
data(data_NorthernPike)
data_nop.mark <- plyr::rename(data_NorthernPike, c("cap_hist"="ch"))
head(data_nop.mark)
## ch length Sex freq
## 1 01 23.20 M 1
## 2 01 28.89 F 1
## 3 01 25.20 M 1
## 4 01 22.20 M 1
## 5 01 25.00 M 1
## 6 01 24.70 M 1# We will be fitting some closed population models the "Closed" models, so we need to know
# the parameters of the model
setup.parameters("Huggins", check=TRUE) # returns a vector of parameter names (case sensitive)
## [1] "p" "c"
# Notice that there is NO parameter for the population size in the Huggins model
nop.sex.time <- mark( data_nop.mark, invisible=TRUE,
model="Huggins",
groups=c("Sex"), # note name must match case and that used in convert.inp command
model.name="model sex*..time",
model.parameters=list(p=list(formula=~Sex*time, share=TRUE))
)
##
## Output summary for Huggins model
## Name : model sex*..time
##
## Npar : 4
## -2lnL: 7391.653
## AICc : 7399.655
##
## Beta
## estimate se lcl ucl
## p:(Intercept) -1.7728555 0.1146487 -1.9975670 -1.5481441
## p:SexM -0.1366869 0.1732879 -0.4763313 0.2029574
## p:time2 -2.0214971 0.0464885 -2.1126145 -1.9303797
## p:SexM:time2 0.2462124 0.0686219 0.1117135 0.3807113
##
##
## Real Parameter p
## 1 2
## Group:SexF 0.1451876 0.0220025
## Group:SexM 0.1290323 0.0244869
##
##
## Real Parameter c
## 2
## Group:SexF 0.0220025
## Group:SexM 0.0244869
summary(nop.sex.time, se=TRUE)
## Output summary for Huggins model
## Name : model sex*..time
##
## Npar : 4
## -2lnL: 7391.653
## AICc : 7399.655
##
## Beta
## estimate se lcl ucl
## p:(Intercept) -1.7728555 0.1146487 -1.9975670 -1.5481441
## p:SexM -0.1366869 0.1732879 -0.4763313 0.2029574
## p:time2 -2.0214971 0.0464885 -2.1126145 -1.9303797
## p:SexM:time2 0.2462124 0.0686219 0.1117135 0.3807113
##
##
## Real Parameter p
## all.diff.index par.index estimate se lcl ucl fixed
## p gF t1 1 1 0.1451876 0.0142288 0.1194586 0.1753545
## p gF t2 2 2 0.0220025 0.0023065 0.0179080 0.0270073
## p gM t1 3 3 0.1290323 0.0146031 0.1030094 0.1604533
## p gM t2 4 4 0.0244869 0.0029329 0.0193509 0.0309430
##
##
## Real Parameter c
## all.diff.index par.index estimate se lcl ucl fixed
## c gF t2 5 2 0.0220025 0.0023065 0.0179080 0.0270073
## c gM t2 6 4 0.0244869 0.0029329 0.0193509 0.0309430
nop.sex.time$results$real
## estimate se lcl ucl fixed note
## p gF t1 0.1451876 0.0142288 0.1194586 0.1753545
## p gF t2 0.0220025 0.0023065 0.0179080 0.0270073
## p gM t1 0.1290323 0.0146031 0.1030094 0.1604533
## p gM t2 0.0244869 0.0029329 0.0193509 0.0309430
nop.sex.time$results$derived
## $`N Population Size`
## estimate se lcl ucl
## 1 27860.51 2700.213 23140.38 33780.31
## 2 21524.51 2406.304 17382.86 26878.68The estimated population size is derived from a HT-type estimator for each sex, and we need to find the total, manually:
cat("\n\n*** Total population size and se from model sex*time\n")
##
##
## *** Total population size and se from model sex*time
temp <- nop.sex.time$results$derived
sum(nop.sex.time$results$derived$`N Population Size`[,"estimate",drop=FALSE])
## [1] 49385.02
sqrt(sum(nop.sex.time$results$derived.vcv$`N Population Size`))
## [1] 3616.83420.6 Example - Northern Pike - Model with length as a covariate
We first standardize the length variable and create a new variable for \(length^2\).
# we standardize the length and l2 variables
data_nop.mark$L <- scale(data_nop.mark$length)
data_nop.mark$L2<- data_nop.mark$L**2
head(data_nop.mark)
## ch length Sex freq L L2
## 1 01 23.20 M 1 -0.7146489 0.5107230
## 2 01 28.89 F 1 0.3710705 0.1376933
## 3 01 25.20 M 1 -0.3330252 0.1109058
## 4 01 22.20 M 1 -0.9054607 0.8198591
## 5 01 25.00 M 1 -0.3711876 0.1377802
## 6 01 24.70 M 1 -0.4284311 0.1835532Now we fit the model:
nop.mtLL <- mark( data_nop.mark, invisible=TRUE,
model="Huggins",
# groups=c("Sex"), # note name must match case and that used in convert.inp command
model.name="model time*(L+L2)",
model.parameters=list(p=list(formula=~time*L+time*L2, share=TRUE))
)
##
## Output summary for Huggins model
## Name : model time*(L+L2)
##
## Npar : 6
## -2lnL: 7150.663
## AICc : 7162.668
##
## Beta
## estimate se lcl ucl
## p:(Intercept) -1.7120281 0.1064007 -1.9205734 -1.5034829
## p:time2 -1.5005707 0.0434446 -1.5857222 -1.4154193
## p:L 0.1734418 0.1311218 -0.0835569 0.4304405
## p:L2 -0.2486361 0.1391712 -0.5214118 0.0241395
## p:time2:L 0.1027038 0.0463942 0.0117711 0.1936365
## p:time2:L2 -0.5414320 0.0453611 -0.6303398 -0.4525242
##
##
## Real Parameter p
## 1 2
## 0.1233986 0.0179409
##
##
## Real Parameter c
## 2
## 0.0179409
summary(nop.mtLL, se=TRUE)
## Output summary for Huggins model
## Name : model time*(L+L2)
##
## Npar : 6
## -2lnL: 7150.663
## AICc : 7162.668
##
## Beta
## estimate se lcl ucl
## p:(Intercept) -1.7120281 0.1064007 -1.9205734 -1.5034829
## p:time2 -1.5005707 0.0434446 -1.5857222 -1.4154193
## p:L 0.1734418 0.1311218 -0.0835569 0.4304405
## p:L2 -0.2486361 0.1391712 -0.5214118 0.0241395
## p:time2:L 0.1027038 0.0463942 0.0117711 0.1936365
## p:time2:L2 -0.5414320 0.0453611 -0.6303398 -0.4525242
##
##
## Real Parameter p
## all.diff.index par.index estimate se lcl ucl fixed
## p g1 t1 1 1 0.1233986 0.0124748 0.1009541 0.1500005
## p g1 t2 2 2 0.0179409 0.0019345 0.0145176 0.0221533
##
##
## Real Parameter c
## all.diff.index par.index estimate se lcl ucl fixed
## c g1 t2 3 2 0.0179409 0.0019345 0.0145176 0.0221533
nop.mtLL$results$real
## estimate se lcl ucl fixed note
## p g1 t1 0.1233986 0.0124748 0.1009541 0.1500005
## p g1 t2 0.0179409 0.0019345 0.0145176 0.0221533The usual estimates of the population size are obtained:
nop.mtLL$results$derived
## $`N Population Size`
## estimate se lcl ucl
## 1 59207.34 9364.158 43877.6 81051.75
cat("\n\n*** Total population size and se from model\n")
##
##
## *** Total population size and se from model
sum(nop.mtLL$results$derived$`N Population Size`[,"estimate"])
## [1] 59207.34
sqrt(sum(nop.mtLL$results$derived.vcv$`N Population Size`))
## [1] 9364.158We can now obtain predictions of the capture probabilities at the two sampling occasions:
pred.length <- seq(from=min(data_nop.mark$L), to=max(data_nop.mark$L), length.out=40)
P.by.length.mtLL <- covariate.predictions(nop.mtLL,
data=data.frame(L=pred.length, L2=pred.length^2), indices=c(1,2))
P.by.length.mtLL$estimates[1:5,]
## vcv.index model.index par.index L L2 estimate se
## 1 1 1 1 -2.088494 4.361808 0.0407473768 0.0261971249
## 2 2 2 2 -2.088494 4.361808 0.0007200627 0.0004620906
## 3 3 1 1 -1.951501 3.808356 0.0475436972 0.0267135981
## 4 4 2 2 -1.951501 3.808356 0.0011574729 0.0006535652
## 5 5 1 1 -1.814508 3.292439 0.0549217128 0.0267342837
## lcl ucl fixed
## 1 0.0112911463 0.136443938
## 2 0.0002046225 0.002530600
## 3 0.0154645439 0.136913096
## 4 0.0003825261 0.003496867
## 5 0.0207375220 0.137541422
ggplot(data=P.by.length.mtLL$estimates, aes(x=L, y=estimate, color=as.factor(par.index)))+
geom_point()+
geom_line()+
xlab("Standardized Length (in)")+ylab("P(capture)")+
scale_color_discrete(name="Event")21 Appendix D. Conditional likelihood approach to tag-loss studies.
We follow the approach of Hyan et al (2012) by looking at the case of 2 indistinguishable tags. The cases of distinguishable or a permanent tag is similar and not presented here.
Figure 28 shows the fates of fish in the tag loss model with 2 indistinguishable tags.
In this diagram, the capture probabilities are denoted by \(p_1\), and \(p_2\), the probability of a single tag being applied is \(S\), and the tag loss probabilities are denoted by \(\rho\). The codes \(A\) and \(B\) denote fish with single and double tags applied in the first sample.
The probability of the capture histories are:
- \(P(1010) = p_1 S (1-\rho) p_2\) = single tag fish recaptured with tag present = \(m_A\)
- \(P(1000) = p_1 S \rho + p_1 S (1-\rho)(1-p_2)\) - single tag fish never seen again (either tag lost or not captured at event 2)
- \(P(1111) = p_1 (1-S) (1-\rho)^2 p_2\) = double tagged fish recaptured with both tags present \(m_{BB}\)
- \(P(111X) = p_1 (1-S) 2 \rho (1-\rho) p_2\) = double tagged fish recaptured with only tag present. There are two ways in which a single tag can be lost = \(m_B\).
- \(P(1100) = p_1 (1-S) \rho^2 + p_1 (1-S) 2\rho(1-\rho)(1-p_2) + p_1 (1-S) (1-\rho)^2(1-p_2)\) = double tagged fish lost both tags or retained at least one tag and was never captured at time 2
- \(P(0010) = p_1 S (1-\rho)p_2 + p_1 (1-S) \rho^2 p_2 + (1-p_1) p_2\) = probability of an apparently untagged fish being captured at event 2 = \(m_U\).
Notice that some fish can be double counted, i.e. fish that were single tagged and never seen again also includes fish that were captured at event 2 after loosing its tag; and fish that were double tagged and never seen again, also includes fish that were captured at event 2 after loosing both tags. Consequently, a full multinomial model cannot be constructed because the probabilities add to more than 1.
However, suppose we condition on being captured at event 2. This corresponds to fish with histories 1010, 1111, 111x, and 0010. This has total probability of \(p_2\).
The conditional probabilities are now
- \(P(1010~|~\textit{captured at event 2}) = p_1 S (1-\rho)\)
- \(P(1111~|~\textit{captured at event 2}) = p_1 (1-S) (1-\rho)^2\)
- \(P(111X~|~\textit{captured at event 2}) = p_1 (1-S) 2 \rho (1-\rho)\)
- \(P(0010~|~\textit{captured at event 2}) = p_1 S (1-\rho)p_2 + p_1 (1-S) \rho^2 p_2 + (1-p_1)\)
Now a conditional maximum likelihood approach can be used to estimate \(p_1\) and \(\rho\) in a similar fashion as the conditional maximum likelihood Lincoln-Petersen estimator.
Once estimates of \(p_1\) are obtained, the estimated abundance is formed using a Horvitz-Thompson type estimator
\[\widehat{N} = \sum_{\textit{animals captured at event 1}} {\frac{1}{\widehat{p}_{1i}}}\]
Estimates of the uncertainty of the abundance estimates are formed again similar to those in the conditional likelihood Petersen estimator.
The main advantage of the conditional likelihood approach is that models where the capture/tag retention parameters vary by covariates that are unknown for fish never seen can be fit again similar to the conditional likelihood Petersen estimator.
22 Appendix E: Brief theory for BTSPAS models.
The complete theory for the BTSPAS models is presented in Bonner and Schwarz (2011). This is a synopsis.
We consider the two cases – the diagonal and non-diagonal cases.
22.1 Diagonal case
In the diagonal model, the relevant data are:
- \(n_{1i}\) - the number released in temporal stratum \(i\)
- \(m_{2i}\) - the number from those releases temporal stratum \(i\) that are captured together in a single future temporal stratum
- \(u2_i\) - the number of UNmarked fish captured in a future temporal stratum along with the recaptures from releases in temporal stratum \(i\).
The capture history data can be structured as:
We can extract the two temporal strata and make a matrix of releases and recoveries of the form:
Recovery Stratum
Never rs1 rs2 rs3 ... rsk Tagged
Newly seen again
Untagged u2[1] u2[2] u2[3] ... u2[k]
captured
Marking ms1 n1[1]-m2[1] m2[1] 0 0 ... 0 n1[1]
Stratum ms2 n1[1]-m2[2] 0 m2[2] 0 ... 0 n1[2]
ms3 n1[1]-m2[3] 0 0 m2[3] ... 0 n1[3]
...
msk n1[1]-m2[k] 0 0 0 ... m2[k] n1[k]
Here the tagging and recapture events have been stratified into \(k\) temporal strata. Marked fish from one stratum tend to move at similar rates and so are recaptured together with unmarked fish. Recaptures of marked fish take place along the “diagonal” as shown below for the first 10 temporal strata:
Note that while this model is referred to as the diagonal model, it is not strictly necessary that recaptures/captures take place in the same temporal stratum as releases. For example, fish could be released in julian week 21 of a calendar year, but take 2 weeks to move to the next fish wheel for recapture in julian week 23. similarly, fish released in julian week 22, are then recaptured in julian week 24, etc. In this case the two-week offset is “hidden” from the program and we “pretend” that releases and recaptures take place in the same temporal stratum.
The Bayesian model has two components. First, we condition on the number of releases and model the recaptures as Binomial distributions: \[m_{2i} \sim Binomial(n_{1i}, p_{2i})\] This is similar to a fully stratified Petersen estimator. However, we assume that the recapture probabilities come from a hierarchical model on the \(logit()\) scale: \[logit(p_{2i}) \sim Normal(\mu, \sigma)\]
The advantage of the hierarchical model is that inference for the parameters in one stratum will depend on the data from all strata. For example, if the data suggests that all of the strata have \(p\)’s close to .025, then this information is used to improve estimates for strata with poor data (or no data at all). In this way, data is shared among the strata, but the parameters are still allowed to vary among strata. The disadvantage of the hierarchical approach is that it makes no adjustment for the ordering of the data – the same amount of information is shared between strata 1 and 2 as strata 1 and 10 or strata 1 and 100. Various extensions to the BTSPAS model could be developed to account for this autocorrelation, but in practice, we have not found it necessary. This follows the framework of Mantyniemi and Romakkaniemi (2002).
Second, we model the unmarked fish captured at the “second” event also by a binomial distribution with the same (re)capture probabilities \[u_{2i} \sim Binomial(U_{2i}, p_{2i})\] where \(U_{2i}\) is the population abundance of unmarked fish passing the second trap along with fish released in temporal stratum \(i\). Again, this is similar to the fully stratified-Petersen estimator. However, it seems intuitive that the number of fish passing the recapture trap will be more similar for strata that are close together and less similar for strata that are further apart. To account for this structure, we impose smoothness on the \(U_{2i}\) using a spline that allows for a very general shape.
Bonner and Schwarz (2011) chose to model \(U_{2i}\) explicitly as a smooth curve using the Bayesian penalized spline (P-spline) method of Lang and Brezger (2004). Two factors control the smoothness of a spline: the number and locations of the knots and the variation in the coefficients of the basis-function expansion. The classical P-spline method of Eilers and Marx (1996) approaches this dichotomy by fixing a large number of knot points and then penalizing the first or second order differences of the coefficients. In the original implementation, the spline curve is fit by minimizing a target function which adds the sum-of-squared residuals and a penalty term formed as the product of a smoothing parameter and the sum of the differences of the spline coefficients. Increasing the smoothing parameter places more weight on the penalty term and results in a smoother curve. Decreasing the smoothing parameter places more weight on the sum-of-squared residuals and produces a fit that comes closer to interpolating the data.
Although the spline model may reflect the trend in the daily population size, similar to a running mean, it is unlikely that \(U_{2i}\) will exactly follow a smooth curve. If the deviations from a smooth curve are small then it seems reasonable that forcing \(U_{2i}\) to be smooth will not have a large impact on the estimation of overall abundance . However, if there are large deviations from the smooth curve then forcing the \(U_{2j}\) to be smooth may severely bias the estimate of the total population size. To allow for roughness in the \(U_{2i}\) over-and-above the spline fit, the spline model is extended with an additional “error” (extra variation) term to allow the \(U_{2i}\) to vary above and below the spline.
Bonner (2008, Section 2.2.4) conducted an extensive simulation study to compare the Bayesian P-spline method with the stratified-Petersen estimator. Generally, the Bayesian P-spline method had negligible bias and its precision was at least as good as the stratified-Petersen estimator. When “perfect” data were available (i.e., many marked fish were released and recaptured in each stratum) the results from the Bayesian P-spline and the stratified-Petersen were very similar. When few marked fish were released or recaptured in each stratum, the performance of the Bayesian P-spline model depended on the amount of variation between the capture probabilities and the pattern of abundance over time. In the worst case, with large variations between the capture probabilities and abundances that followed no regular patterns, the two models continued to perform similarly. However, when the variation between the capture probabilities were smaller and the abundances followed close to a smooth curve the Bayesian P-spline produced much more precise estimates of the total population size.
22.2 Non-diagonal case
In many cases, the released fish are not recaptured in a single future temporal stratum, and recaptures takes place for a number of future strata.
This gives rise to the matrix of releases and recoveries of the form:
Recovery Stratum
Newly
Untagged u2[1] u2[2] u2[3] ... u2[k] u2[k,k+1]
captured
tagged rs1 rs2 rs3 ...rs4 rsk rs(k+1)
Marking ms1 n1[1] m2[1,1] m2[1,2] m2[1,3] m2[1,4] 0 ... 0 0
Stratum ms2 n1[2] 0 m2[2,2] m2[2,3] m2[2,4] .... 0 ... 0 0
ms3 n1[3] 0 0 m2[3,3] m2[3,4] ... 0 ... 0 0
...
msk n1[k] 0 0 0 ... 0 0 m2[k,k] m2[k,k+1]
In the above representation, released fish take between 0 and 3 weeks to travel between the two traps between release and recapture.
BTSPAS includes a function to fit a log-normal distribution to the length of time that individual fish take to move between the temporal stratum of release and temporal stratum of recovery, but this model may not be sufficiently flexible. Alternatively, BTSPAS includes a function that uses a multinomial distribution to describe the movement of fish from the temporal release stratum to the temporal recovery stratum with the restriction that this multinomial movement model slowly changes over time.
GIVE MORE DETAILS HERE
The hierarchical model for the recapture probabilities and the smoothing spline are similar in this non-diagonal non-parametric movement model.